NIST NCSTAR 1-6C

Federal Building and Fire Safety Investigation of the

World Trade Center Disaster

Component, Connection, and

Subsystem Structural Analysis

Mehdi S. Zarghamee,

Said Bolourchi

Daniel W. Eggers

Omer O. Erbay

Frank W. Kan

Yasuo Kitane

Peter R. Barrett

John L. Gross

Therese P. McAllister

Atis A. Liepins

Michael Mudlock

Wassim I. Naguib

Rasko P. Ojdrovic

Andrew T. Sarawit

National Institute of Standards and Technology • Technology Administration • U.S. Department of Commerce

NISTNCSTAR1-6C

Federal Building and Fire Safety Investigation of the

World Trade Center Disaster

Component, Connection, and

Subsystem Structural Analysis

Mehdi S. Zarghamee

Said Bolourchi, Daniel W. Eggers, Omer O. Erbay, Frank W. Kan, Yasuo Kitane,

Atis A. Liepins, Michael Mudlock, Wassim I. Naguib, Rasko P. Ojdrovic, and Andrew T. Sarawit

Simpson Gumpertz & Heger Inc.

Peter R. Barrett Computer Aided Engineering Associates, Inc.

John L. Gross

Therese P. McAllister

Building and Fire Research Laboratory

National Institute of Standards and Technology

September 2005

U.S. Department of Commerce

Carlos M. Gutierrez, Secretary

Technology Administration

Michelle O'Neill, Acting Under Secretary for Technology

National Institute of Standards and Technology

William Jeffrey, Director
Disclaimer No. 1

Certain commercial entities, equipment, products, or materials are identified in this document in order to describe a procedure or concept adequately or to trace the history of the procedures and practices used. Such identification is not intended to imply recommendation, endorsement, or implication that the entities, products, materials, or equipment are necessarily the best available for the purpose. Nor does such identification imply a finding of fault or negligence by the National Institute of Standards and Technology.

Disclaimer No. 2 The policy of NIST is to use the International System of Units (metric units) in all publications. In this document,

however, units are presented in metric units or the inch-pound system, whichever is prevalent in the discipline.

Disclaimer No. 3

Pursuant to section 7 of the National Construction Safety Team Act, the NIST Director has determined that certain evidence received by NIST in the course of this Investigation is "voluntarily provided safety-related information" that is "not directly related to the building failure being investigated" and that "disclosure of that information would inhibit the voluntary provision of that type of information" (15 USC 7306c).

In addition, a substantial portion of the evidence collected by NIST in the course of the Investigation has been

provided to NIST under nondisclosure agreements.

Disclaimer No. 4 NIST takes no position as to whether the design or construction of a WTC building was compliant with any code

since, due to the destruction of the WTC buildings, NIST could not verify the actual (or as-built) construction, the

properties and condition of the materials used, or changes to the original construction made over the life of the

buildings. In addition, NIST could not verify the interpretations of codes used by applicable authorities in determining

compliance when implementing building codes. Where an Investigation report states whether a system was

designed or installed as required by a code provision, NIST has documentary or anecdotal evidence indicating

whether the requirement was met, or NIST has independently conducted tests or analyses indicating whether the requirement was met.

Use in Legal Proceedings

No part of any report resulting from a NIST investigation into a structural failure or from an investigation under the

National Construction Safety Team Act may be used in any suit or action for damages arising out of any matter mentioned in such report (15 USC 281a; as amended by P.L. 107-231).

National Institute of Standards and Technology National Construction Safety Team Act Report 1-60

Natl. Inst. Stand. Technol. Natl. Constr. Sfty. Tm. Act Rpt. 1-60, 251 pages (September 2005)

CODEN: NSPUE2

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 2005

For sale by the Superintendent of Documents, U.S. Government Printing Office

Internet: bookstore.gpo.gov — Phone: (202) 512-1800 — Fax: (202) 512-2250

Mail: Stop SSOP, Washington, DC 20402-0001
Abstract

Simpson Gumpertz & Heger, Inc. (SGH) developed finite element models of the components,

connections and subsystems of the World Trade Center (WTC) towers to study their structural performance in the fire environment that followed the aircraft impact to the towers. The results of this study were used to develop global models that captured with numerical efficiency the important failure modes and sequential failures of components and subsystems and to determine the probable sequence of

structural responses that let to the global collapse initiation. The study was conducted as part of the

investigation on the WTC disaster by the National Institute of Standards and Technology (NIST).

The structural response to the fire environment was established by hand calculations and finite element

analyses (FEA) for: connections including interior and exterior truss seats, knuckles, column splices, and

spandrel sphces; components including a section of the floor system, including concrete slab and a single

truss and a single coluirm, and subsystems including full floors and a section exterior wall. The key

structural responses, failure modes, and failure loads were identified.

The finite element models, developed in ANSYS, captured the nonlinear responses of the comiections,

components, and subsystems, including temperature-dependent material properties such as thennal

expansion, plasticity and creep of metals, large deflection and the resulting instability, and failure modes

of members and connections, modeled by break elements developed for this purpose. The models were

subjected to gravity and thermal loads. Construction sequence was included in component models. NIST

provided temperature-dependent nonlinear material properties, aircraft impact damage to structural members, and temperature time histories of structural elements for subsystems, which were used as input

in this study.

The nonlinear analysis of a section of floor system, including break elements that represented the

strucmral performance of interior and exterior truss seats and knuckles, showed that the floor sagged

when subjected to high temperatures beyond 600 °C; the main cause of the floor sagging was buckling of

truss web diagonals. The sagging floors pulled in the exterior walls. Floor/wall disconnections occurred

by the truss walking off their seats after failure of all horizontal connections between the floor and the

exterior wall, or by the vertical shear failure of the truss seat, as its capacity was reduced by heat.

The column analysis showed that exterior columns spanning a single floor at low temperatures were

susceptible to premature buckling initiated by local buckling of plates with rapid reduction of load

carrying capacity in the post-buckling regime. This failure mode did not exist when the column was

spanning more than one floor or was at high temperatures.

The nonlinear model of the full floor system was developed in ANSYS by converting the existing linear

SAP2000 model and by modifying the model to capture the failure modes and the failure loads calculated

in the study of components in the fire environment and to enhance computational efficiency. The

enhancement was achieved for example by combining double trusses into a single truss to enhance

computational efficiency. The model was subjected to the gravity loads and the temperature time

histories provided by NIST. The results of analyses performed for all floors with thermal loads showed

that the key structural responses of the floors under fire were 1 ) floor sagging resuhing in pull-in forces

between the floor and the exterior wall, and 2) disconnections of the floors from the exterior walls.

NISTNCSTAR 1-6C, WTC Investigation iii
Abstract

A nonlinear model of a section of the exterior wall subsystem consisting of nine floors in height and nine

columns in width was developed, including large deflection and inelastic buckling of columjis and

spandrels and failure of their splices. The model was subjected to gravity loads, including the column

loads and NIST provided temperature time histories. The results of the analyses showed that instability of

the wall system did not occur when the wall was braced at every floor or when the floor did not restrain the out-of-plane motion of the exterior wall for up to three floors. Bowing and buckling occurred when

the wall was subjected to increased column loads or to floor/wall pull-in forces. Furthennore, the exterior

column splice failure was rare and occurred by opening of the splices in bending; only in one case was

sliding experienced without bolt failure at high temperatures and high vertical loads. Large deformation

and buckling of spandrels and partial separations of the spandrel splices were also found in the analysis,

but they did not significantly affect the stability of the exterior columns.

Keywords: Collapse, creep, large deflection, nonlinear finite element analysis, plasticity, structural response to damage, structural response to fire, stability, World Trade Center.

IV NISTNCSTAR 1-6C, WTC Investigation
Table of Contents

Abstract iii

List of Figures ix

List of Tables xvii

List of Acronyms and Abbreviations xix

Preface xxi

Acknowledgements xxxi

Executive Summary xxxiii

Chapter 1 Introduction 1

1.1 Purpose 1

1.2 Scope of Work 1

1.3 Report Organization 1

Chapter 2

Description of Subsystem Structures 3

2. 1 Full Floor Subsystem Description 3

2.2 Exterior Wall Subsystem Description 6

2.3 Loads 7

Chapter 3 Materials 9

3.1 Concrete 9

3.1.1 Concrete Properties 9

3.1.2 Concrete Stress-Strain Relationships 10

3.1.3 Concrete Failure Criteria 1

3.2 Steel 13

3.2.1 Steel Properties 13

3.2.2 Stress-Strain Relationship 13

3.2.3 Steel Failure Criteria 19

3.3 Welds 21

3.4 Bolts 21

3.5 Coefficient of Friction 22

NISTNCSTAR 1-6C, WTC Investigation v
Table of Contents

3.6 Symbols 22

Chapter 4

Model Conversion From SAP to ANSYS 25

4. 1 Translation Procedure 25

4.2 Validation 28

4.2.1 Floor Model Validation 28

4.2.2 Global Model Validation 33

4.3 Summary 37

Chapter 5 Full Floor Subsystem 39

5.1 Objective 39

5.2 Truss Seats 39

5.2.1 Description of Truss Seats 39

5.2.2 Truss Seat Material Properties 41

5.2.3 Truss Seat Failure Modes and Sequence 42

5.2.4 Truss Seat Capacity Calculations 46

5.2.5 Modeling Failure by Break Elements 53

5.2.6 Summary of Failure Modes and Finite Element Models of Truss Seats 55

5.2.7 Sunmiary of Failure Modes and Finite Element Models of the Stud on Strap Anchor and

Spandrel Stud 59

5.3 Knuckle Analysis 61

5.3.1 Description of Knuckle 61

5.3.2 Failure Modes of Knuckle 61

5.3.3 Knuckle Shear Tests 61

5.3.4 Finite Element Model for Knuckle Test 63

5.3.5 Material Properties for Knuckle Analysis 63

5.3.6 Results from Knuckle Analysis 64

5.3.7 Summary of Failure Modes and Finite Element Models of Knuckle Model for Truss Model 67

5.4 Truss Model. 69

5.4.1 Model Description 69

5.4.2 Failure Modes.... 71

5.4.3 Boundary Conditions 71

5.4.4 Loads 73

5.4.5 Material Properties 73

vi NIST NCSTAR 1-6C, WTC Investigation
Table of Contents

5.4.6 Resistance Welds 74

5.4.7 Model Verification 75

5.4.8 Truss Analysis for Debris Load 75

5.4.9 Truss Analysis for Gravity and Thermal Loads 77

5.4.10 Simplified Truss Model 84

5.5 Full Floor Model 86

5.5.1 Objective 86

5.5.2 Failure Modes 86

5.5.3 Model Description 86

5.5.4 Material Properties 90

5.5.5 User-Defined Break Elements 91

5.5.6 Impact Damage 95

5.5.7 Gravity' and Thermal Loads 107

5.5.8 Boundary Conditions 117

5.5.9 Results from WTC 1 Floor 96 under Case Aj Temperature Condition 1 17

5.5.10 Results from Other WTC 1 Floors under Case A, Temperature Condition 122

5.5.1 1 Results from WTC 1 Floors under Case B, Temperature Condition 127

5.5.12 Results from WTC 2 Floor 82 under Case C, Temperature Condition 133

5.5.13 Results from Other WTC 2 Floors under Case C, Temperature Condition 138

5.5.14 Results from WTC 2 Floors under Case Dj Temperature Condition 142

5.5.15 Creep Effect 148

5.5.16 Effect of Column Boundary Conditions 148

5.5.17 Floor Subsystem in Global Models 149

5.5.18 Summary of Results and Discussion 155

Chapter 6 Exterior Wall Subsystem 157

6.1 Objective 157

6.2 Exterior Wall Subsystem Description 157

6.3 Failure Modes 161

6.4 Model Validation 161

6.4.1 Description of Models 161

6.4.2 Validation Results 164

6.5 Finite-Element Model of Exterior Wall Subsystem 165

6.5.1 Elements and Meshing 165

NIST NCSTAR 1-6C. WTC Investigation vii
Table of Contents

6.5.2 Boundary Conditions 166

6.5.3 One-, Two-, and Three-Story High Columns 168

6.5.4 Spandrel Splices 171

6.5.5 Column Splices 173

6.5.6 Loads 174

6.6 Analysis Cases 1 76

6.7 Analysis Results 177

6.7.1 Columns Braced at All Floors 177

6.7.2 Columns Not Braced at Floors 95 and 96 185

6.7.3 Columns Not Braced at Floors 95, 96, and 97 186

6.7.4 Columns Not Braced and Pulled at Unbraced Floors 95, 96, and 97 188

6.7.5 Columns Not Braced at Floors 95, 96, and 97 and Pushed Down at Top 191

6.8 Summai'y and Discussion of Exterior Wall Analysis Results 196

6.8. 1 Columns Braced at All Floors 196

6.8.2 Columns Not Braced at Floors 95 and 96 196

6.8.3 Columns Not Braced at Floors 95, 96, and 97 196

6.8.4 Coluinns Not Braced and Pulled in at Floors 95, 96, and 97 197

6.8.5 Columns Not Braced at Floors 95, 96, and 97 and Columns Pushed Down at Top 197

6.8.6 Summary of Analysis Results 198

6.9 Summary of Results 198

Chapter 7 Modeling Details for Subsystems in Global Models 201

Chapter 8 References 203

vm NISTNCSTAR 1-6C, WTC Investigation
List of Figures

Figure P-1 . The eight projects in the federal building and fire safety investigation of the WTC

disaster xxiii

Figure 2-1. Mock up of office floor framing system (Photograph from about 1967 provided by

Laclede Steel Co.) 4

Figure 2-2. Floor plan of Floor 96 of WTC 1 5

Figure 2-3. Exterior wall construction with prefabricated wall panels 7

Figure 3-1 . Properties of concrete that vary with temperature 11

Figure 3-2. Concrete stress-strain relationships at different temperatures 12

Figure 3-3. Properties for all steel types that vary with temperature 14

Figure 3—4. Steel (Material ID 1) stress-strain relationships at different temperatures 16

Figure 3-5. Comparison of creep strains with a{T) given by (7-a) and (7-d) for Material ID 1

steel subject to 15 ksi for 1,800 s at a given temperature 18

Figure 3-6. Creep behavior at elevated temperatures for Material ID 1 steel 19

Figure 3-7. Maximum plastic strain from the finite element analysis and limiting plastic strain 21

Figure 3-8. 7/8 in. A325 bolt load-elongation curves at elevated temperatures 22

Figure 4-1. Converted ANSYS model for Floor 96 of WTC 1: overall view 28

Figure 4-2. Converted ANSYS model for Floor 96 of WTC 1 : partial view near comer of

building 29

Figure 4-3. Converted ANSYS model for Floor 96 of WTC 1 : close-up view at comer of

building 29

Figure 4-4. Converted ANSYS model for Floor 96 of WTC 1 : view of floor beams and columns 30

Figure 4-5. Deformed shape (xlOO) of gravity load case for SAP floor model (downward

displacement is negative) 30

Figure 4-6. Deformed shape (xlOO) of gravity load case for ANSYS floor model (total

displacements are shown) 31

Figure 4-7. Dominant mode shape (frequency = 4.32 Hz) of floor stmcture for SAP floor model 32

Figure 4-8. Dominant mode shape (frequency = 4.43 Hz) of floor stmcture for ANSYS floor

model 32

Figure 4-9. Converted ANSYS model of WTC 1 34

Figure 4-10. Converted ANSYS model of WTC 2 34

Figure 4-11. Displaced shape of WTC I at the end of gravity analysis 35

NISTNCSTAR 1-6C, WTC Investigation ix
List of Figures

Figure 4-12. Displaced shape of WTC 2 at the end of gravity analysis 35

Figure 5-1 . Interior truss seat 40

Figure 5-2. Exterior truss seat 40

Figure 5-3. Truss seat detail location on northeast quadrant of Floor 96 of WTC 1 41

Figure 5-4. Finite element model of exterior truss seat 43

Figure 5-5. Failure sequence of the exterior truss seats against tensile force 44

Figure 5-6. Capacity of exterior truss seat for tensile force (Path (A) in Fig. 5-5 for Detail

1411) 45

Figure 5-7. Truss seat capacity for vertical force 48

Figure 5-8. Truss seat capacity for horizontal tensile force 51

Figure 5-9. Capacity of interior truss seat against vertical and horizontal force (for Detail 22) 52

Figure 5-10. Basic mathematical model of connection failure 54

Figure 5-1 1 . Representation of interior truss seat by break elements 56

Figure 5-12. Results of interior truss seat model capturing failure from truss walking off the seat at 500 T 57

Figure 5-13. Results of interior truss seat model capturing failure from exceeding the vertical

shear capacity at 500 °C 57

Figure 5-14. Representation of exterior truss seat by break elements 58

Figure 5-15. Location of stud on strap anchor and spandrel stud 59

Figure 5-16. Representation of stud shear connector by break elements 60

Figure 5-17. Longitudinal shear test of a knuckle 62

Figure 5-18. Transverse shear test of a knuckle 63

Figure 5-19. Finite element models of knuckle shear tests 64

Figure 5-20. Compressive stresses in longitudinal shear finite element model (4,100 psi concrete) 65

Figure 5-21. Shear force versus displacement from finite element model for longitudinal shear of

two knuckles (4,100 psi concrete) 65

Figure 5-22. Compressive stresses in transverse shear finite element model (2,500 psi concrete) 66

Figure 5-23. Shear force versus displacement from finite element model for transverse shear of

two knuckles (2,500 psi concrete) 66

Figure 5-24. Representation of knuckle by break elements 68

Figure 5-25. Truss model 70

Figure 5-26. Boundary conditions 72

Figure 5-27. Break elements at the interior end of slab 72

Figure 5-28. Assumed Temperature Distribution in the Truss Model at 30 min 73

X NISTNCSTAR 1-6C, WTC Investigation
List of Figures

Figure 5-29. Comparison of resistance weld strength and yield strength of web member at elevated temperatures 75

Figure 5-30. Finite element analysis results from increasing gravity 76

Figure 5-31. Vertical displacement at 700 °C (downward displacement is negative) 77

Figure 5-32. Displacement versus temperature of steel 78

Figure 5-33. Element numbers and locations of elements examined for axial force 79

Figure 5-34. Axial force in truss members versus temperature of steel 80

Figure 5-35. Axial stress contour in the truss members at 700 °C (tension is positive; l.Ox

displacement magnification) 81

Figure 5-36. Force in the knuckles versus temperature of steel 82

Figure 5-37. Horizontal reaction forces 83

Figure 5-38. Comparison of detailed and simplified truss models 85

Figure 5-39. Full floor model without impact damage 88

Figure 5—40. Full floor model after removal of deck support angles, spandrel studs, bridging

trusses outside of two-way zones, and strap anchors 90

Figure 5^1 . Bilinear material model for concrete slab in the full floor model 91

Figure 5—42. Bilinear material model in the spandrel 91

Figure 5—43. Summary of user-defined break element locations in the full floor model 93

Figure 5^4. User-defined break element locations in the full floor model (Floor 96, WTC 1 ) 94

Figure 5-45. Case Aj insulation damage condition for WTC 1 floor trusses and beams 96

Figure 5^6. Case A, structural damage condition for WTC 1 floors 97

Figure 5^7. Structural damage to exterior walls of WTC 1 for Case A, and Case Bj impact

damage conditions 98

Figure 5—48. Structural damage to core columns of WTC 1 for Case A, impact damage condition 99

Figure 5-49. Case C, insulation damage condition for WTC 2 floor trusses and beams 100

Figure 5-50. Case C, structural damage condition for WTC 2 floors 101

Figure 5-5 1 . Case D, insulation damage condition for WTC 2 floor trusses and beams 1 02

Figure 5-52. Case D, structural damage condition for WTC 2 floors 103

Figure 5-53. Structural damage to exterior walls of WTC 2 for Case C, and Case D, impact

damage conditions 104

Figure 5-54. Structural damage to core columns of WTC 2 for Case C, impact damage condition 104

Figure 5-55. Case A, structural impact damage condifion for exterior columns of the north face in the WTC 1 Floor 96 model 105

Figure 5-56. Case A, structural impact damage condition for exterior columns of the south face in the WTC 1 Floor 96 model 105

Figure 5-57. Case Aj structural impact damage condition for floor trusses in the WTC 1 Floor 96

model 106

NISTNCSTAR 1-6C. WTC Investigation xi
List of Figures

Figure 5-58. Case Aj structural impact damage condition for the concrete slab in the WTC 1 Floor

96 model 106

Figure 5-59. Case A, structural impact damage condition for core beams in the WTC 1 Floor 96

model 107

Figure 5-60. Case A, structural impact damage condition for core columns in the WTC 1 Floor 96

model ^ 107

Figure 5-61. Design live load distribution in Floor 96 of WTC 1 108

Figure 5-62. Case A, temperature condition for Floor 96 of WTC 1 at 10 min, 50 min, and

100 min 109

Figure 5-63. Case A, temperature distribution in the slab for Floor 96 of WTC 1 at 10 min,

50 min, and 100 min 110

Figure 5-64. Case B, temperature condition for Floor 96 of WTC 1 at 10 min, 50 min, and

100 min Ill

Figure 5-65. Case B, temperature distribution in the slab for Floor 96 of WTC 1 at 10 min, 50 min,

and 100 min 112

Figure 5-66. Case C, temperature condition for Floor 82 of WTC 2 at 10 min, 30 min, and 60 min 113

Figure 5-67. Case C, temperature distribution in the slab for Floor 82 of WTC 2 at 10 min, 30 min,

and 60 min 114

Figure 5-68. Case D, temperature condition for Floor 82 of WTC 2 at 10 min, 30 min, and 60 min 115

Figure 5-69. Case D, temperature distribution in the slab for Floor 82 of WTC 2 at 10 min,

30 min, and 60 min 116

Figure 5-70. Vertical displacement of WTC 1 Floor 96 for Case A, temperature condition at 10 min, 50 min, and 100 min (downward displacement is negative; 5x displacement

magnification) 119

Figure 5-71. Horizontal displacement of exterior columns of Floor 96 of WTC 1 for Case Aj

temperature condition at 10 min, 50 min, and 100 min 120

Figure 5-72. Horizontal reaction force per column of WTC 1 Floor 96 for Case A, temperature

condition 121

Figure 5-73. User-defined break elements that failed by 100 min in the model of WTC 1 Floor 96

for Case A, temperature condition 121

Figure 5-74. Vertical displacement of WTC 1 Floor 93 for Case A, temperature condition at 30 min (downward displacement is negative; 5x displacement magnification) 123

Figure 5-75. Vertical displacement of WTC 1 Floor 94 for Case Aj temperature condition at 100 min (downward displacement is negative; 5x displacement magnification). 124

Figure 5-76. Vertical displacement of WTC 1 Floor 95 for Case Aj temperature condition at 10 min (downward displacement is negative; 5x displacement magnification) 124

Figure 5-77. Vertical displacement of WTC 1 Floor 97 for Case A, temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 125

Figure 5-78. Vertical displacement of WTC 1 Floor 98 for Case Ai temperature condition at 30 min (downward displacement is negative; 5x displacement magnification). 125

xii NISTNCSTAR 1-6C. WTC Investigation
List of Figures

Figure 5-79. Vertical displacement of WTC 1 Floor 99 for Case A, temperature condition at 50 min (downward displacement is negative; 5x displacement magnification). 126

Figure 5-80. Average thermal expansion of WTC 1 floors at 100 min for Case A, temperature

condition 126

Figure 5-8 1 . Horizontal reaction force per column of WTC 1 Floor 97 for Case A, temperature

condition 127

Figure 5-82. Vertical displacement of WTC 1 Floor 93 for Case B, temperature condition at 100 min (downward displacement is negative; 5x displacement magnification). 128

Figure 5-83. Vertical displacement of WTC 1 Floor 94 for Case Bj temperature condition at 100 min (downward displacement is negative; 5x displacement magnification). 129

Figure 5-84. Vertical displacement of WTC 1 Floor 95 for Case Bj temperamre condition at 10 min (downward displacement is negative; 5x displacement magnification) 129

Figure 5-85. Vertical displacement of WTC 1 Floor 96 for Case Bi temperature condition at 10 min (downward displacement is negative; 5x displacement magnification) 130

Figure 5-86. Vertical displacement of WTC 1 Floor 97 for Case B, temperature condition at 100 min (downward displacement is negative; 5x displacement magnification) 130

Figure 5-87. Vertical displacement of WTC 1 Floor 98 for Case Bi temperature condition at 100 min (downward displacement is negative; 5x displacement magnification) 131

Figure 5-88. Vertical displacement of WTC 1 Floor 99 for Case B, temperature condition at 100 min (downward displacement is negative; 5x displacement magnification) 131

Figure 5-89. Loss of vertical supports in Floor 97 and Floor 98 of WTC 1 for Case B, temperature

condition at 100 min (Ix displacement magnification) 132

Figure 5-90. Thermal expansion of WTC 1 floors at 100 min for Case B, conditions 132

Figure 5-9 1 . Horizontal reaction force per column of WTC 1 Floor 96 for Case Bj temperature

condition 133

Figure 5-92. Horizontal reaction force per column of WTC 1 Floor 98 for Case Bj temperature

condition 133

Figure 5-93. Vertical displacement of WTC 2 Floor 82 for Case C, temperature condition at 10 min, 30 min, and 60 min (downward displacement is negative; 5x displacement

magnification) 135

Figure 5-94. Horizontal displacement of exterior columns of WTC 2 Floor 82 for Case Cj

temperature condition at 10 min, 30 min, and 60 min 136

Figure 5-95. Total horizontal reaction at exterior columns on east and west faces of WTC 2 Floor

82 for Case C, conditions 137

Figure 5-96. User-defined break elements that failed by 60 min in the model of WTC 2 Floor 82

for Case C, temperature condition 137

Figure 5-97. Loss of vertical supports in Floor 82 of WTC 2 for Case C, temperature condition at 60 min (Ix displacement magnification) 138

Figure 5-98. Vertical displacement of WTC 2 Floor 79 for Case Cj temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 139

NISTNCSTAR 1-6C, WTC Investigation xiii
List of Figures

Figure 5-99. Vertical displacement of WTC 2 Floor 80 for Case Q temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 140

Figure 5-100. Vertical displacement of WTC 2 Floor 81 for Case C, temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 140

Figure 5-101. Vertical displacement of WTC 2 Floor 83 for Case C, temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 141

Figure 5-102. Average thermal expansion of WTC 2 floors at 60 min under Case C, temperature

condition 141

Figure 5-103. Horizontal reaction force per column of WTC 2 Floor 81 for Case C, temperature

condition 142

Figure 5-104. Loss of vertical supports in Floor 83 of WTC 2 for Case Cj temperature condition at 60 min (3X displacement magnification) 142

Figure 5-105. Vertical displacement of WTC 2 Floor 79 for Case D, temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 144

Figure 5-106. Vertical displacement of WTC 2 Floor 80 for Case Dj temperature condition at 40 min (downward displacement is negative; 5x displacement magnification) 144

Figure 5-107. Vertical displacement of WTC 2 Floor 81 for Case Dj temperature condition at 50 min (downward displacement is negative; 5x displacement magnification) 145

Figure 5-108. Vertical displacement of WTC 2 Floor 82 for Case D, temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 145

Figure 5-109. Vertical displacement of WTC 2 Floor 83 for Case D, temperature condition at 60 min (downward displacement is negative; 5x displacement magnification) 146

Figure 5-110. Horizontal reaction force per column of WTC 2 Floor 80 for Case D, temperature

condition 146

Figure 5-1 1 1. Horizontal reaction force per column of WTC 2 Floor 82 for Case D, temperature

condition 147

Figure 5-112. Average thermal expansion of WTC 2 floors at 60 min for Case D, temperature

condition 147

Figure 5-1 13. Vertical displacement of a simplified truss model at Column 333 extracted from the

full floor model of Floor 96 of WTC 1 under Case B, temperature condition at 40 min

(downward displacement is negative) 148

Figure 5-1 14. Conditions of connections between the exterior wall and the floors of WTC 1 for

Case A, temperature condition at 100 min 151

Figure 5-115. Conditions of connections between the exterior wall and the floors of WTC 1 for Case B, temperature condition at 100 min 152

Figure 5-116. Conditions of connections between the exterior wall and the floors of WTC 2 for Case C, temperature condition at 60 min 153

Figure 5-117. Conditions of connections between the exterior wall and the floors of WTC 2 for

Case D, temperature condition at 60 min 154

Figure 6-1 . Exterior wall subsystem structure 158

xiv NISTNCSTAR 1-6C, WTC Investigation
List of Figures

Figure 6-2. Columns, spandrels, and splices: type and material assignments 159

Figure 6-3. Schematic of column cross section 160

Figure 6-4. SAP2000 model of prefabricated panel 1 62

Figure 6-5. ANSYS model of prefabricated panel showing meshing 163

Figure 6-6. ANSYS model of prefabricated panel showing boundary conditions and loading

(loads applied separately) 163

Figure 6-7. Deflection of prefabricated panel under 100 kip lateral load 164

Figure 6-8. Deflection of prefabricated panel under 100 kip transverse load 164

Figure 6-9. Deflection of prefabricated panel under 10 kip vertical load 165

Figure 6-10. Exterior wall subsystem model with boundary conditions 166

Figure 6-11. Tj'pical meshing of exterior wall model components 167

Figure 6-12. Schematic representation of columns used in the exterior wall model 167

Figure 6-13. One-story exterior column model 169

Figure 6-14. Load-deflection of column at room temperature and 700 °C 169

Figure 6-15. Local buckling of column at room temperature 170

Figure 6-16. Plastic hinge in column at room temperature 170

Figure 6-17. Deformed shape of column at maximum axial load at 700 °C 171

Figure 6-18. Typical spandrel sphce layout for exterior wall subsystem 172

Figure 6-19. Modeling of a typical interior spandrel sphce in the exterior wall model 172

Figure 6-20. Column splice model used in exterior wall model 173

Figure 6-2 1 . Exterior wall model temperature time-histories 1 75

Figure 6-22. Structural response for temperature time history D with all floors supported 178

Figure 6-23. Structural response for temperature time history DBARE with all floors supported 179

Figure 6-24. Structural response for temperamre time history E (hot bolts) with all floors supported 181

Figure 6-25. Structural response for temperature time history El 19 with all floors supported 182

Figure 6-26. Structural response for temperature time histor\- F with all floors supported 184

Figure 6-27. Structural response for temperature time history DBARE with two unbraced floors 185

Figure 6-28. Structural response for time history DBAR£ with three unbraced floors 187

Figure 6-29. Structural response for temperature time history DBARE with pull-in forces at three

floors (lOX displacement magnification) 189

Figure 6-30. Column splice bolt stresses for temperature time history and DBARE with pull-in

forces at three floors 1 90

Figure 6-3 1 . Column splice contact element status for temperature time history and DBARE with

pull-in forces at three floors 190

NISTNCSTAR 1-6C, WTC investigation xv
List of Figures

Figure 6-32. Structural response for temperature time history DBARE and push-down with tliree unbraced floors (lOX displacement magnification) 192

Figure 6-33. Column splice response for temperature time history DBARE and push-down with

tliree unbraced floors 192

Figure 6-34. Sum of total column reaction forces at base during push-down after application of

temperature DBARE with three unbraced floors 193

Figure 6-35. Sum of additional vertical reaction forces at base induced by imposed displacement

during push-down after application of temperature DBARE with three unbraced

floors 193

Figure 6-36. Individual total column reaction forces at base during push-down after application of

temperature DBARE with three unbraced floors 194

Figure 6-37. Individual additional column reaction forces at base induced by imposed vertical

displacement during push-down after application of temperature DBARE with three

unbraced floors 194

Figure 6-38. Difference between the additional individual column reaction forces at base and the

vertical force applied at the top of each column during push-down after application of

temperature DBARE with three unbraced floors 195

Figure 6-39. Transverse deflection during push-down after application of temperature DBARE

with three unbraced floors 195

xvi NISTNCSTAR 1-6C, WTC Investigation
List of Tables

Table P-1 . Federal building and fire safety investigation of the WTC disaster xxii

Table P-2. Public meetings and briefings of the WTC Investigation xxv

Table 3-1 . Steel types used in WTC 1 and WTC 2 1

Table 3-2. Parameters for K(T) and n(T) 16

Table 3-3. Uniaxial plastic strain at fracture by Eq. (11) 20

Table 4—1 . Element types used in ANSYS models 27

Table 4-2. Comparison of SAP and ANSYS results for gravity load case 28

Table 4-3. Comparison of SAP and ANSYS floor model modal analysis results 3

Table 4—4. Comparison of maximum displacements and base reactions of WTC 1 from

translated ANSYS and SAP2000 models 36

Table 4-5. Comparison of maximum displacements and base reactions of WTC 2 obtained from

translated ANSYS and SAP2000 models 36

Table 4-6. Comparison of axial forces in randomly selected elements from WTC 1 model at the

end of gravity analysis 36

Table 4-7. Comparison of axial forces in randomly selected elements from WTC 2 model at the

end of gravity analysis 37

Table 5-1 . Materials used for truss seat calculations 42

Table 5-2. Exterior truss seat capacity for vertical force 47

Table 5-3. Interior truss seat capacity for vertical force 47

Table 5-4. Exterior truss seat capacity for horizontal tensile force 50

Table 5-5. Interior truss seat capacity against horizontal tensile force 50

Table 5-6. Compression strength of gusset plate 52

Table 5-7. Temperature-dependent knuckle capacity for assumed temperatures 67

Table 5-8. Material assignments in truss model 74

Table 5-9. Resistance weld strength 74

Table 5-10. Types of user-defined break elements 92

Table 5-11. Number of user-defined break elements in the full floor model (Floor 96, WTC 1 ) 94

Table 5-12. List of full floor model analyses performed 117

Table 5-13. Number of failed user-defined break elements in the model of WTC 1 Floor 96 for Case A, temperature condition 122

NISTNCSTAR 1-6C, WTC Investigation xvii
List of Tables

Table 5-14. Maximum vertical displacement of WTC 1 floors for Case Aj temperature condition. ... 123

Table 5-15. Maximum vertical displacement of WTC 1 floors for Case Bj temperature condition 128

Table 5-16. Number of failed user-defined break elements in the model of WTC 2 Floor 82 for Case Cj temperature condition 138

Table 5-17. Maximum vertical displacement of WTC 2 floors for Case Cj temperature condition 139

Table 5-18. Maximum vertical displacement of WTC 2 floors for Case D, temperature condition 143

Table 6-1 a. Column sectional properties 160

Table 6- lb. Column splice details 160

Table 6-1 c. Spandrel splice details 161

Table 6-2. Prefabricated panel validation results 165

Table 6-3. Thermal loading conditions used in the exterior wall model 175

Table 6-4. Analysis cases for exterior wall subsystem model 177

Table 6-5. Summary of spandrel splice break elements for temperature time history D with all floors supported. 178

Table 6-6. Summary of spandrel splice break elements for temperature time history DBARE

with all floors supported 180

Table 6-7. Summary of spandrel splice break elements for temperature time-history E (hot

bolts) with all floors supported 181

Table 6-8. Summary of spandrel splice break elements for temperature time history El 19 with

all floors supported 183

Table 6-9. Summary of spandrel splice break elements for temperature time history F with all floors supported 184

Table 6-10. Summary of spandrel splice break elements for temperature time history DBARE

with 2 unbraced floors 186

Table 6-1 1 . Spandrel splice break elements for temperature time history DBARE with 3 unbraced floors 187

Table 6-12. Summary of exterior wall model results 198

xviii NISTNCSTAR 1-6C, WTC Investigation
List of Acronyms and Abbreviations

Acronyms

ARA Applied Research Associates, Inc. ASTM American Society for Testing and Materials

BPS Building Performance Study

CAEAI Computer Aided Engineering Associates, Inc. FEMA Federal Emergency Management Agency

FEA Finite element analysis

LERA Leslie E. Robertson Associates

NIST National Institute of Standards and Technology

PANYNJ The Port Authority of New York and New Jersey

SEAoNY Structural Engineers Association of New York

SGH Simpson Gumpertz & Heger Inc. use United States Code

WTC World Trade Center

WTC 1 World Trade Center 1 (North Tower)

WTC 2 World Trade Center 2 (South Tower)

WTC 7 World Trade Center 7

Abbreviations

X degrees Celsius

°F degrees Fahrenheit

ft feet

in. inch

L liter m meter

micrometer

h hour

min minute

s second

lb pound

NISTNCSTAR 1-6C, WTC Investigation xix
List of Acronyms and Abbreviations

kip kilo pounds

pcf pound per cubic foot

psf pound per square foot

psi pound per square inch

ksi kilo pounds per square inch

XX NISTNCSTAR 1-6C, WTC Investigation
Preface

Genesis of This Investigation

Immediately following the terrorist attack on the World Trade Center (WTC) on September 11, 2001, the

Federal Emergency Management Agency (FEMA) and the American Society of Civil Engineers began

plaiming a building performance study of the disaster. The week of October 7, as soon as the rescue and

search efforts ceased, the Building Performance Study Team went to the site and began its assessment. This was to be a brief effort, as the study team consisted of experts who largely volunteered their time

away from their other professional commitments. The Building Performance Study Team issued its report in May 2002, fulfilling its goal "to determine probable failure mechanisms and to identify areas of

future investigation that could lead to practical measures for improving the damage resistance of buildings

against such unforeseen events." On August 21. 2002, with funding from the U.S. Congress through FEMA, the National Institute of

Standards and Technology (NIST) announced its building and fire safety investigation of the WTC

disaster. On October 1, 2002. the National Construction Safety Team Act (Public Law 107-231), was

signed into law. The NIST WTC Investigation was conducted under the authority of the National

Construction Safety Team Act.

The goals of the investigation of the WTC disaster were:

• To investigate the building construction, the materials used, and the technical conditions that contributed to the outcome of the WTC disaster.

• To ser\'e as the basis for: - Improvements in the way buildings are designed, constructed, maintained, and used; - Improved tools and guidance for industry and safety officials; - Recommended revisions to current codes, standards, and practices; and - Improved public safety.

The specific objectives were:

1 . Determine why and how WTC 1 and WTC 2 collapsed following the initial impacts of the

aircraft and why and how WTC 7 collapsed;

2. Determine why the injuries and fatahties were so high or low depending on location,

including all technical aspects of fire protection, occupant behavior, evacuation, and

emergency response;

3. Determine what procedures and practices were used in the design, construction, operation,

and maintenance of WTC 1, 2, and 7; and

4. Identify, as specifically as possible, areas in current building and fire codes, standards, and

practices that warrant revision.

NISTNCSTAR 1-6C, WTC Investigation XXI
Preface

NIST is a nonregulatory agency of the U.S. Department of Commerce's Technology Administration. The

purpose of NIST investigations is to improve the safety and structural integrity of buildings in the United

States, and the focus is on fact finding. NIST investigative teams are authorized to assess building

performance and emergency response and evacuation procedures in the wake of any building failure that has resulted in substantial loss of life or that posed significant potential of substantial loss of life. NIST

does not have the statutory authority to make findings of fault nor negligence by individuals or

organizations. Further, no part of any report resulting from a NIST investigation into a building failure or from an investigation under the National Construction Safety Team Act may be used in any suit or action

for damages arising out of any matter mentioned in such report (15 USC 281a, as amended by Public

Law 107-231).

Organization of the Investigation

The National Construction Safety Team for this Investigation, appointed by the then NIST Director, Dr. Arden L. Bement, Jr., was led by Dr. S. Shyam Sunder. Dr. William L. Grosshandler served as Associate Lead Investigator, Mr. Stephen A. Cauffman sei'ved as Program Manager for Administration,

and Mr. Harold E. Nelson served on the team as a private sector expert. The Investigation included eight

interdependent projects whose leaders comprised the remainder of the team. A detailed description of

each of these eight projects is available at http://wtc.nist.gov. The purpose of each project is summarized

in Table P-1, and the key interdependencies among the projects are illustrated in Fig. P-1.

Table P-1. Federal building and fire safety investigation of the WTC disaster.

Technical Area and Project Leader Project Purpose

Analysis of Building and Fire Codes and

Practices; Project Leaders: Dr. H. S. Lew

and Mr. Richard W. Bukowski

Document and analyze the code provisions, procedures, and

practices used in the design, construction, operation, and

maintenance of the stmctural. passive fire protection, and

emergency access and evacuation systems of WTC 1, 2, and 7. Baseline Structural Performance and

Aircraft Impact Damage Analysis; Project

Leader: Dr. Fahim H. Sadek

Analyze the baseline performance of WTC 1 and WTC 2 under

design, service, and abnormal loads, and aircraft impact damage on

the structural, fire protection, and egress systems.

Mechanical and Metallurgical Analysis of

Structural Steel; Project Leader: Dr. Frank

W. Gayle

Determine and analyze the mechanical and metallurgical properties

and quality of steel, weldments, and connections from steel recovered from WTC 1,2, and 7. Investigation of Active Fire Protection

Systems; Project Leader: Dr. David

D. Evans; Dr. William Grosshandler

Investigate the performance of the active fire protection systems in WTC 1, 2, and 7 and their role in fire control, emergency response, and fate of occupants and responders.

Reconstruction of Thermal and Tenability

Environment; Project Leader: Dr. Richard

G. Gann

Reconstruct the time-evolving temperature, thermal environment,

and smoke movement in WTC 1, 2, and 7 for use in evaluating the

structural performance of the buildings and behavior and fate of

occupants and responders.

Structural Fire Response and Collapse

Analysis; Project Leaders: Dr. John

L. Gross and Dr. Therese P. McAllister

Analyze the response of the WTC towers to fires with and without

aircraft damage, the response of WTC 7 in fires, the performance

of composite steel-trussed floor systems, and determine the most

probable structural collapse sequence for WTC 1. 2. and 7. Occupant Behavior, Egress, and Emergency

Communications; Project Leader: Mr, Jason D. Averill

Analyze the behavior and fate of occupants and responders, both

those who survived and those who did not, and the performance of

the evacuation system.

Emergency Response Technologies and

Guidelines; Project Leader: Mr. J. Randall

Lawson

Document the activities of the emergency responders from the time

of the terrorist attacks on WTC 1 and WTC 2 until the collapse of

WTC 7, including practices followed and technologies used.

xxii NISTNCSTAR 1-6C, WTC Investigation
Preface

NIST WTC Investigation Projects

Figure P-1. The eight projects in the federal building and fire safety

investigation of the WTC disaster.

National Construction Safety Team Advisory Committee

The NIST Director also established an advisory committee as mandated under the National Construction

Safety Team Act. The initial members of the committee were appointed following a public solicitation. These were:

• Paul Fitzgerald, Executive Vice President (retired) FM Global, National Construction Safety

Team Advisory Committee Chair

• John Barsom, President, Barsom Consulting, Ltd.

• John Bryan, Professor Emeritus, University of Maryland

• David Collins. President, The Preview Group, Inc.

• Glenn Corbett, Professor, John Jay College of Criminal Justice

• Philip DiNenno, President, Hughes Associates, Inc.

NISTNCSTAR 1-6C. WTC Investigation xxni
Preface

• Robert Hanson, Professor Emeritus, University of Michigan

• Charles Thornton, Co-Chairman and Managing Principal, The Thomton-Tomasetti Group,

Inc.

• Kathleen Tiemey, Director, Natural Hazards Research and Applications Information Center,

University of Colorado at Boulder

• FoiTnan Williams, Director, Center for Energy Research, University of California at San

Diego

This National Construction Safety Team Advisory Committee provided technical advice during the

Investigation and commentary on drafts of the Investigation reports prior to their public release. NIST

has benefited from the work of many people in the preparation of these reports, including the National

Construction Safety Team Advisory Committee. The content of the reports and recommendations,

however, are solely the responsibility of NIST.

Public Outreach

During the course of this Investigation, NIST held public briefings and meetings (listed in Table P-2) to

solicit input from the public, present preliminary findings, and obtain comments on the direction and

progress of the Investigation from the public and the Advisory Committee.

NIST maintained a publicly accessible Web site during this Investigation at http://wtc.nist.gov. The site contained extensive information on the background and progress of the Investigation.

NIST's WTC Public-Private Response Plan

The collapse of the WTC buildings has led to broad reexamination of how tall buildings are designed,

constructed, maintained, and used, especially with regard to major events such as fires, natural disasters,

and terrorist attacks. Reflecting the enhanced interest in effecting necessary change, NIST, with support

from Congress and the Administration, has put in place a program, the goal of which is to develop and

implement the standards, technology, and practices needed for cost-effective improvements to the safety

and security of buildings and building occupants, including evacuation, emergency response procedures,

and threat mitigation.

The strategy to meet this goal is a three-part NIST-led public-private response program that includes:

• A federal building and fire safety investigation to study the most probable factors that contributed to post-aircraft impact collapse of the WTC towers and the 47-story WTC 7

building, and the associated evacuation and emergency response experience.

• A research and development (R&D) program to (a) facilitate the implementation of

recommendations resulting from the WTC Investigation, and (b) provide the technical basis

for cost-effective improvements to national building and fire codes, standards, and practices

that enhance the safety of buildings, their occupants, and emergency responders.

xxiv NISTNCSTAR 1-6C, WTC Investigation
Preface

Table P-2. Public meetings and briefings of the WTC Investigation.

Date Location Principal Agenda

June 24. 2002 New York City, NY Public meeting: Public coinments on the Draft Plan for the pending WTC Investigation.

August 21. 2002 Gaithersburg. MD Media briefing announcing the formal start of the Investigation.

December 9. 2002 Washington, DC Media briefing on release of the Public Update and NIST request

for photographs and videos. Apnl 8. 2003 New York City, NY Joint public forum with Columbia University on first-person interviews. April 29-30. 2003 Gaithersburg, MD NCST Advisory Committee meeting on plan for and progress on WTC Inx'estigation with a public comment session. May 7. 2003 New York City. NY Media briefing on release of May 2003 Progress Report.

August 26-27, 2003 Gaithersburg, MD NCST Advisory Committee meeting on status of the WTC

investigation with a public comment session. September 17. 2003 New York City. NY Media and public briefing on initiation of first-person data

collection projects.

December 2-3. 2003 Gaithersburg, MD NCST Advisory Committee meeting on status and initial results and release of the Public Update with a public comment session. February' 12. 2004 New York City, NY Public meeting on progress and preliminary findings with public

comments on issues to be considered in fonnulating final recommendations.

June 18. 2004 New York City. NY Media public briefing on release of June 2004 Progress Report. June 22-23. 2004 Gaithersburg, MD NCST Advisory Committee meeting on the status of and

preliminary findings from the WTC Investigation with a public

comment session. August 24, 2004 Northbrook, IL Public \'iew ing of standard fire resistance test of WTC floor system at Underwriters Laboratories. Inc. October 19-20. 2004 Gaithersburg. MD NCST Advisory Cominittee meeting on status and near complete

set of preliminary findings with a public coinment session. November 22. 2004 Gaithersburg. MD NCST Advisory Committee discussion on draft annual report to Congress, a public comment session, and a closed session to discuss pre-draft recommendations for WTC Investigation.

April 5. 2005 New York City, NY Media and public briefing on release of the probable collapse sequence for the WTC towers and draft reports for the projects on

codes and practices, evacuation, and emergency response. June 23, 2005 New York City, NY Media and public briefing on release of all draft reports for the WTC towers and draft recommendations for public comment.

September 12-13,

2005

Gaithersburg, MD NCST Advisory Committee meeting on disposition of pubhc

comments and update to draft reports for the WTC towers. September 13-15,

2005

Gaithersburg, MD WTC Technical Conference for stakeholders and technical community for dissemination of findings and recommendations

and opportunity for public to make technical comments.

• A dissemination and technical assistance program (DTAP) to (a) engage leaders of the

construction and building community in ensuring timely adoption and widespread use of

proposed changes to practices, standards, and codes resulting from the WTC Investigation

and the R&D program, and (b) provide practical guidance and tools to better prepare facility owners, contractors, architects, engineers, emergency responders, and regulatory authorities

to respond to future disasters. The desired outcomes are to make buildings, occupants, and first responders safer in future disaster events.

NISTNCSTAR 1-6C, WTC Investigation XXV
Preface

National Construction Safety Team Reports on the WTC Investigation

A final report on the collapse of the WTC towers is being issued as NIST NCSTAR 1. A companion

report on the collapse of WTC 7 is being issued as NIST NCSTAR lA. The present report is one of a set that provides more detailed documentation of the Investigation findings and the means by which these

technical results were achieved. As such, it is part of the archival record of this Investigation. The titles of the full set of Investigation publications are:

NIST (National Institute of Standards and Technology). 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Final Report on the Collapse ofthe World Trade

Center Towers. NIST NCSTAR 1. Gaithersburg, MD, September.

NIST (National Institute of Standards and Technology). 2006. Federal Building and Fire Safety

Investigation of the World Trade Center Disaster: Final Report on the Collapse of World Trade Center 7. NISTNCSTAR 1 A. Gaithersburg, MD.

Lew, H. S., R. W. Bukowski, and N. J. Carino. 2005. Federal Building and Fire Safety Investigation of

the World Trade Center Disaster: Design, Construction, and Maintenance ofStructural and Life Safety

Systems. NIST NCSTAR 1-1. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Fanella, D. A., A. T. Derecho, and S. K. Ghosh. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Design and Construction ofStructural Systems.

NIST NCSTAR 1-1 A. National Institute of Standards and Teclinology. Gaithersburg, MD,

September.

Ghosh, S. K., and X. Liang. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Comparison ofBuilding Code Structural Requirements. NIST

NCSTAR 1-lB. National Institute of Standards and Technology. Gaithersburg, MD, September.

Fanella, D. A., A. T. Derecho, and S. K. Ghosh. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Maintenance and Modifications to Structural

Systems. NIST NCSTAR 1-1 C. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Fire Protection and Life Safety Provisions Applied to the Design and

Construction of World Trade Center 1, 2, and 7 and Post-Construction Provisions Applied after Occupancy. NIST NCSTAR 1-lD. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Razza, J. C, and R. A. Grill. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Comparison of Codes, Standards, and Practices in Use at the Time ofthe

Design and Construction of World Trade Center 1, 2, and 7. NIST NCSTAR 1-lE. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Grill, R. A., D. A. Johnson, and D. A. Fanella. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Comparison ofthe 1968 and Current (2003) New

xxvi NISTNCSTAR 1-6C, WTC Investigation
Preface

York City Building Code Provisions. NIST NCSTAR 1-lF. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Amendments to the Fire Protection and Life Safety Provisions ofthe New

York City Building Code by Local Laws Adopted While World Trade Center 1, 2, and 7 Were in Use. NIST NCSTAR 1-1 G. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Grill. R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Post-Construction Modifications to Fire Protection and Life Safety Systems

of World Trade Center I and 2. NIST NCSTAR 1-lH. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Grill, R. A., D. A. Johnson, and D. A. Fanella. 2005. Federal Building and Fire Safety' Investigation

ofthe World Trade Center Disaster: Post-Construction Modifications to Fire Protection, Life

Safety, and Structural Systems of World Trade Center 7. NIST NCSTAR l-ll. National Institute of

Standards and Technology. Gaithersburg, MD, September.

Grill, R. A., and D. A. Johnson. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Design, Installation, and Operation ofFuel System for Emergency Power in World Trade Center 7. NIST NCSTAR 1-1 J. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Sadek, F. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center Disaster:

Baseline Structural Performance and Aircraft Impact Damage Analysis ofthe World Trade Center

Towers. NIST NCSTAR 1-2. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Faschan, W. J., and R. B. Garlock. 2005. Federal Building and Fire Safety Investigation ofthe

World Trade Center Disaster: Reference Structural Models and Baseline Performance Analysis of

the World Trade Center Towers. NIST NCSTAR 1-2A. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Kirkpatrick, S. W., R. T. Bocchieri, F. Sadek, R. A. MacNeill, S. Holmes, B. D. Peterson, R. W. Cilke, C. Navarro. 2005. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Analysis ofAircraft Impacts into the World Trade Center Towers, NIST

NCSTAR 1-2B. National Institute of Standards and Technology. Gaithersburg, MD, September.

Gayle, F. W.. R. J. Fields, W. E. Luecke, S. W. Banovic, T. Foecke, C. N. McCowan, T. A. Siewert, and

J. D. McColskey. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Mechanical and Metallurgical Analysis ofStructural Steel. NIST NCSTAR 1-3. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Luecke, W. E., T. A. Siewert, and F. W. Gayle. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Contemporaneous Stmctural Steel

Specifications. NIST Special Publication 1-3 A. National Institute of Standards and Technology.

Gaithersburg, MD, September.

NIST NCSTAR 1-6C, WTC Investigation xxvii
Preface

Banovic, S. W. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Steel Inventory and Identification. NIST NCSTAR 1-3B. National Institute of Standards

and Technology. Gaithersburg, MD, September.

Banovic, S. W., and T. Foecke. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Damage and Failure Modes ofStructural Steel Components. NIST

NCSTAR 1-3C. National Institute of Standards and Technology. Gaithersburg, MD, September.

Luecke, W. E., J. D. McColskey, C. N. McCowan, S. W. Banovic, R. J. Fields, T. Foecke,

T. A. Siewert, and F. W. Gayle. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Mechanical Properties ofStructural Steels. NIST NCSTAR 1-3D.

National Institute of Standards and Technology. Gaithersburg, MD, September.

Banovic, S. W., C. N. McCowan, and W. E. Luecke. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Physical Properties ofStructural Steels. NIST

NCSTAR 1-3E. National Institute of Standards and Technology. Gaithersburg, MD, September.

Evans, D. D., R. D. Peacock, E. D. Kuligowski, W. S. Dols, and W. L. Grosshandler. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Active Fire Protection

Systems. NIST NCSTAR 1-4. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Kuligowski, E. D., D. D. Evans, and R. D. Peacock. 2005. Federal Building and Fire Safety

Investigation of the World Trade Center Disaster: Post-Construction Fires Prior to September 11,

2001. NIST NCSTAR 1-4A. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Hopkins, M., J. Schoenrock, and E. Budnick. 2005. Federal Building and Fire Safety Investigation

ofthe World Trade Center Disaster: Fire Suppression Systems. NIST NCSTAR 1-4B. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Keough, R. J., and R. A. Grill. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Fire Alarm Systems. NIST NCSTAR 1-4C. National Institute of Standards

and Technology. Gaithersburg, MD, September.

Ferreira, M. J., and S. M. Strege. 2005. Federal Building and Fire Safety Investigation ofthe

World Trade Center Disaster: Smoke Management Systems. NIST NCSTAR I-4D. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Gann, R. G., A. Hamins, K. B. McGrattan, G. W. Mulholland, H. E. Nelson, T. J. Ohlemiller,

W. M. Pitts, and K. R. Prasad. 2005. Federal Building and Fire Safety^ Investigation ofthe World Trade

Center Disaster: Reconstruction ofthe Fires in the World Trade Center Towers. NIST NCSTAR 1-5. National Institute of Standards and Technology. Gaithersburg, MD, September.

Pitts, W. M., K. M. Butler, and V. Junker. 2005. Federal Building and Fire Safety Investigation of

the World Trade Center Disaster: Visual Evidence, Damage Estimates, and Timeline Analysis.

NIST NCSTAR 1-5A. National Institute of Standards and Technology. Gaithersburg, MD,

September.

xxvm NIST NCSTAR 1-6C, WTC Investigation
Preface

Hamins, A., A. Maranghides, K. B. McGrattan, E. Johnsson, T. J. Ohlemiller, M. Donnelly,

J. Yang. G. MulhoUand, K. R. Prasad, S. Kukuck. R. Anleitner and T. McAllister. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Experiments and

Modeling ofStructural Steel Elements Exposed to Fire. NIST NCSTAR 1-5B. National Institute of

Standards and Technology. Gaithersburg, MD, September.

Ohlemiller, T. J., G. W. Mulholland, A. Maranghides, J. J. Filliben, and R. G. Gann. 2005. Federal

Building and Fire Safety' Investigation ofthe World Trade Center Disaster: Fire Tests ofSingle

Office Workstations. NIST NCSTAR 1-5C. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Gann, R. G.. M. A. Riley, J. M. Repp, A. S. Whittaker, A. M. Reinhom, and P. A. Hough. 2005.

Federal Building and Fire Safety Investigation ofthe World Trade Center Disaster: Reaction of

Ceiling Tile Systems to Shocks. NIST NCSTAR 1-5D. National Institute of Standards and

Technology. Gaithersburg, MD, September.

Hamins, A.. A. Maranghides, K. B. McGrattan, T. J. Ohlemiller, and R. Anleitner. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Experiments and

Modeling ofMultiple Workstations Burning in a Compartment. NIST NCSTAR 1-5E. National

Institute of Standards and Technology. Gaithersburg, MD, September.

McGrattan, K. B., C. Bouldin, and G. Forney. 2005. Federal Building and Fire Safety

Investigation ofthe World Trade Center Disaster: Computer Simulation ofthe Fires in the World

Trade Center Towers. NIST NCSTAR 1-5F. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Prasad, K. R., and H. R. Baum. 2005. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Fire Structure Interface and Thermal Response ofthe World Trade Center

Towers. NIST NCSTAR 1-5G. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Gross, J. L., and T. McAllister. 2005. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Structural Fire Response and Probable Collapse Sequence ofthe World Trade Center

Towers. NIST NCSTAR 1-6. National Institute of Standards and Technology. Gaithersburg, MD,

September.

Carino, N. J., M. A. Stames, J. L. Gross, J. C. Yang, S. Kukuck, K. R. Prasad, and R. W. Bukowski.

2005. Federal Building, and Fire Safety Investigation ofthe World Trade Center Disaster: Passive

Fire Protection. NIST NCSTAR 1-6A. National Institute of Standards and Technology.

Gaithersburg, MD, September.

Gross, J., F. Hervey, M. Izydorek, J. Mammoser, and J. Treadway. 2005. Federal Building and

Fire Safety Investigation ofthe World Trade Center Disaster: Fire Resistance Tests ofFloor Truss

Systems. NIST NCSTAR 1-6B. National Institute of Standards and Technology. Gaithersburg,

MD, September.

Zarghamee, M. S., S. Bolourchi, D. W. Eggers, O. O. Erbay, F. W. Kan, Y. Kitane, A. A. Liepins,

M. Mudlock, W. I. Naguib, R. P. Ojdrovic, A. T. Sarawit, P. R Barrett, J. L. Gross, and

T. P. McAllister. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

NIST NCSTAR 1-6C. WTC Investigation xxix
Preface

Disaster: Component, Connection, and Subsystem Structural Analysis. NISTNCSTAR 1-6C.

National Institute of Standards and Technology. Gaithersburg, MD, September.

' Zarghamee, M. S., Y. Kitane, O. O. Erbay, T. P. McAllister, and J. L. Gross. 2005. Federal

Building and Fire Safety Investigation ofthe World Trade Center Disaster: Global Structural

Analysis ofthe Response ofthe World Trade Center Towers to Impact Damage and Fire. NIST

NCSTAR 1-6D. National Institute of Standards and Technology. Gaithersburg, MD, September.

McAllister, T., R. W. Bukowski, R. G. Gann, J. L. Gross, K. B. McGrattan, H. E. Nelson, L. Phan,

W. M. Pitts, K. R. Prasad, F. Sadek. 2006. Federal Building and Fire Safety Investigation ofthe World

Trade Center Disaster: Structural Fire Response and Probable Collapse Sequence of World Trade

Center 7. (Provisional). NIST NCSTAR 1-6E. National Institute of Standards and Technology.

Gaithersburg, MD.

Gilsanz, R., V. Arbitrio, C. Anders, D. Chlebus, K. Ezzeldin, W. Guo, P. Moloney, A. Montalva,

J. Oh, K. Rubenacker. 2006. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Structural Analysis ofthe Response of World Trade Center 7 to Debris Damage

and Fire. (Provisional). NIST NCSTAR 1-6F. National Institute of Standards and Technology.

Gaithersburg, MD.

Kim, W. 2006. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Analysis ofSeptember II, 2001, Seismogram Data. (Provisional). NIST NCSTAR 1-6G.

National Institute of Standards and Technology. Gaithersburg, MD.

Nelson, K. 2006. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: The Con Ed Substation in World Trade Center 7. (Provisional). NIST NCSTAR 1-6H.

National Institute of Standards and Technology. Gaithersburg, MD.

Averill, J. D., D. S. Mileti, R. D. Peacock, E. D. Kuligowski, N. Groner, G. Proulx, P. A. Reneke, and

H. E. Nelson. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center Disaster:

Occupant Behavior, Egress, and Emergency Communication. NIST NCSTAR 1-7. National Institute of

Standards and Technology. Gaithersburg, MD, September.

Fahy, R., and G. Proulx. 2005. Federal Building and Fire Safety Investigation ofthe World Trade

Center Disaster: Analysis ofPublished Accounts of the World Trade Center Evacuation. NIST

NCSTAR 1-7A. National Institute of Standards and Technology. Gaithersburg, MD, September.

Zmud, J. 2005. Federal Building and Fire Safety Investigation ofthe World Trade Center

Disaster: Technical Documentationfor Sur\>ey Administration. NISTNCSTAR 1-7B. National

Institute of Standards and Technology. Gaithersburg, MD, September.

Lawson, J. R., and R. L. Vettori. 2005. Federal Building and Fire Safety Investigation ofthe

World Trade Center Disaster: The Emergency Response Operations. NIST NCSTAR 1-8. National Institute of Standards and Technology. Gaithersburg, MD, September.

XXX NISTNCSTAR 1-6C, WTC Investigation
Acknowledgements

The assistance of SGH internal Structural Performance Review Committee (Glenn R. Bell, Ronal O.

Hamburger, and Pedro J. Sifre) is gratefully acknowledged. Authors would also like to thank the

technical staff of Computer Aided Engineering Associates, Inc., for their effort at converting SAP2000

finite element models to ANSYS and for their assistance in finite element modeling in ANSYS.

NISTNCSTAR 1-6C, WTC Investigation XXXI
Acknowledgements

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xxxii NISTNCSTAR 1-6C, WTC Investigation
Executive Summary

E.1 INTRODUCTION

Simpson Gumpertz & Heger Inc. (SGH) developed finite-element models of the components, connections

and subsystems of the World Trade Center (WTC) towers to study their structural performance in the fire environment that followed the aircraft impact to the towers. The results of this study were used to develop global models that ran efficiently and captured the important failure modes and sequential

failures of components and subsystems and to determine the probable sequence of structural responses

that let to the global collapse initiation. SGH performed this study under a NIST contract as part of Project 6 of the investigation on the WTC

disaster by the National Institute of Standards and Technology (NIST). This report constitutes SGH

report on Task 1 of the SGH contract with NIST and Part I of the SGH two-part report.

This study completed the following:

• Developed and validated ANSYS models of the full floor and exterior wall subsystems.

• Evaluated structural responses of components, coimections, and subsystems to service loads

due to gra\'ity (dead and live loads) and elevated temperatures.

• Identified the likely failure modes and failure sequences of components, connections, and

subsystems.

• Identified modeling details of the floor and exterior wall subsystems for the global models of

the WTC towers.

All analyses used the nominal dimensions and design details shown on the WTC design and construction

drawings. Material properties were based on information provided from NIST Project 3 study.

E.2 FULL FLOOR SUBSYSTEM

Floor 96 of WTC 1 was identified as an office floor with typical floor construction and loading; therefore,

it was selected as the basis for modeling floor response. Figure E-1 shows a floor plan of Floor 96 of

WTC 1 . The fiill floor subsystem included office area and core area floor framing, as well as core and

exterior columns extending to floors immediately above and below this floor.

The floor system in the office area consisted of lightweight concrete slab supported by steel floor trusses. The steel trusses for the floor system were manufactured by Laclede Steel Co. in Saint Louis, Missouri.

Steel trusses spanned nominally 60 ft in the long-span area and 36 ft in the short-span area between

exterior walls and the central core. Typically, a pair of primary trusses was supported at odd-numbered

columns at 6 ft 8 in. on center. Each of these primary trusses consisted of top and bottom chords

fabricated from double steel angles and web diagonals fabricated from round bars (see Fig. E-2). Web

diagonals extended 3 in. above the top chord at the panel points into the concrete slab to form a knuckle

and to provide shear transfer between the truss and the concrete slab (see Fig. E-2).

NISTNCSTAR 1-6C, WTC Investigation XXXlll
Executive Summary

Exterior column

number

Exterior column

Diagonal strap

anchor

Transfer truss

101 103 106 1CS 112 115 118 121 124 127 130

Short-span

primary

double truss

Long-span

primary

double truss

> Bridging truss

7 Core column

/ and core column number

N

t

Core area

35! 3M 3S1 M JIS 312 359 336 333 330 S27 3»S 321 StB 31S 312 309 SOS SCG 301

Figure E-1 . Floor plan of Floor 96 of WTC 1

XXXIV NISTNCSTAR 1-6C, WTC Investigation
Executive Summary

Primary

double truss

y Bridging truss

Figure E-2. Mock up of office floor framing system (Photograph from about 1967

provided by Laclede Steel Co.).

The top chords of a pair of trusses (double truss) were supported at the central core by an interior truss seat (Fig. E-3) welded to steel channels that ran continuously around the core floor area. Each pair of

trusses was fastened to a horizontal plate of the interior truss seat by two 5/8 in. bolts (one bolt in each

truss) in 1 3/4 in. long slotted holes. At the exterior wall, each pair of trusses was supported by an

exterior truss seat (Fig. E—4). which fastened to a seat angle with two 5/8 in. diameter bolts in 2 in. long

slotted holes. A pair of stand-off plates welded the seat angle to the spandrel. In addition, a gusset plate

welded to the spandrel and to the truss top chord tied the truss to the supporting column, and a pair of

diagonal strap anchors, welded to the top chords and to the adjacent columns, tied these columns to the

primary trusses. Diagonal strap anchors will be referred to as "strap anchors" hereafter.

Primary trusses were interconnected by a transverse system of bridging trusses and deck support angles.

These bridging trusses w ere of similar construction to the primary trusses, except the knuckles did not

project abo\ e the top chords. The top chord of the bridging trusses sat 1 1/2 in. below the top chord of

the primary trusses and provided support for the 4 in. thick lightweight concrete slab on the 1 1/2 in., 22

gauge steel deck with 2 in. wide at the top, 1.25 in. wide at the bottom, and 1.5 in. high flutes at 6.8 in. on

center running parallel to the primary trusses. At each comer of the building core, a 36 ft long transfer

truss extended out from the comer core column to the exterior wall and supported the 60 ft long primary

tmsses. The floor in the core consisted of a 4.5 in. thick lightweight concrete slab supported by wide

flange girders and beams connected to the core columns with bolted connections. Reinforcement between

the core area floor and the office area floor (#3 bars at 10 in. at the top and #4 bars at 12 in. at the bottom,

respectively) provided continuity between the two areas and restrained the truss from walking off the

interior seat.

NISTNCSTAR 1-6C. WTC Investigation XXXV
Executive Summary

Channel beam

Truss top chord

Strut

Truss top chord

Bearing angle

5/8 in. dia. bolt Channel beam

Bearing angle

Horizontal plate

5/8 in. dia. bolt

Vertical plate stiffener Side View

Vertical plate stiffener

Front View Top View

Figure E-3. Interior truss seat.

Column/spandrel

Gusset plate Gusset plate —^ Strut

Truss top chord

Strut

I SO- VBearing angle

5/8 in. diameter bolt

Seat angle

Stand-off plate

Truss top chord

Bearing angle

5/8 in. diameter bolt

Column/spandrel

Gusset plate

Seat angle

5/8 in. dia. bolt

Truss top chord

Stmt

Column/spandrel

Stand-off plate Side View Front View

Figure E-4. Exterior truss seat.

Top View

E.2.1 Truss Seat Analysis

Failure Modes: The failure modes for truss seats were identified for vertical force, horizontal tensile force, horizontal compressive force, and combined vertical and horizontal force, and the corresponding

capacities were calculated for different temperatures as follows:

• Vertical Force: The failure mode of exterior truss seats for vertical force was identified as

fracture of the fillet welds between the stand-off plates and spandrel, which resulted in loss of

truss vertical support. The failure mode of interior truss seats for vertical force was fracture of the fillet welds at the vertical plate to the channel beam. This failure mode results in loss of truss vertical support.

• Horizontal Tensile Force: The failure sequence of the exterior truss seats for horizontal

tensile force differed for different seat details at different temperatures although the final failure mode was truss walk-off for all details. The typical failure sequence of the exterior

truss seat was as follows: the gusset plate yielded, the groove weld yielded, the groove weld

fractured, the truss bearing angle slid, seat bolts came to bear against the slotted hole, the

xxxvi NISTNCSTAR 1-6C, WTC Investigation
Executive Summary

bolts sheared off, and finally the truss walked off the seat angle. The failure sequence of the

interior truss seats for horizontal tensile force was bolt shear-off, resulting in truss walk-off

• Horizontal Compressive Force: Even after the concrete slab failed in compression, additional

resistance was developed from the spandrel at the exterior seat or from the channel beam at the interior seat after contact. Under compressive force, the truss did not lose its vertical

support.

• Combined Vertical and Horizontal Forces: Under combined vertical and horizontal forces,

the failure modes were a combination of the failure modes for vertical and horizontal forces. The vertical shear strength of the truss seats was reduced due to the additional horizontal

tensile force. The horizontal tensile strength was not reduced by the additional vertical force on the seat.

Truss Seat Model for Truss Model: Truss seat capacities corresponding to the failure modes were computed for the different types of the truss seats at different temperatures. Finite element models of the

exterior and interior truss seats were developed for incorporation in the floor truss analysis using "break

elements." Break elements are unidirectional linear springs that were turned off and did not resist any

force after the connection forces reached predefined temperature-dependent capacities.

E.2.2 Knuckle Analysis

Failure Modes: The failure modes of knuckles are:

• Horizontal shear failure due to shear crack or crushing of concrete

• Pullout failure due to vertical tension

The capacities of knuckles were determined based on shear test results conducted by Laclede Steel Co.,

the results of finite element analysis simulating the shear tests, and hand calculations. Knuckle shear and

pullout capacity at room temperature were determined as 30 kip and 15 kip, respectively. Capacities at elevated temperatures were calculated based on knock-down factor on concrete strength at given

temperatures.

Knuckle Model for Truss Model: A model of knuckle was also developed for the truss model, using break

elements.

E.2.3 Truss Analysis

A finite element model of a section of a floor system, which consisted of a single floor truss and a section

of concrete slab with a tributary width, was developed in ANSYS to capture the potential failure modes

and failure sequence of the truss under gravity load and thermal load. The model is referred to as "truss model" in this report.

Failure Modes: Two possible failure modes were identified for the truss model: 1) softening and sagging

of the truss caused by plasticity, creep, and buckling of web diagonal members at high temperatures; and

2) loss of truss vertical support resulting either from seat failure caused by loss of vertical shear capacity

at high temperatures or from truss walking-off truss seat due to large sagging.

Model Description: The truss model included the following:

NISTNCSTAR 1-6C. WTC Investigation XXXVll
Executive Summary

• A single typical long-span truss (C32T1) of the primary double truss at Column 143 at Floor 96 of WTC 1. All steel truss members were modeled by 3-D quadratic finite strain

.

^ beam elements.

• Two exterior columns (Columns 143 and 144) with half the area and bending properties, and

a length of 24 ft ( 12 ft above and below the floor level), using elastic beam elements.

• The portion of the spandrel between the two exterior columns, using elastic shell elements.

• The portion of the slab (40 in. wide) between the two exterior columns. The concrete slab was modeled with 4 layers of 3-D, 8-node structural solid elements for an equivalent

thickness of 4.35 in.

• One strap anchor connected to the truss top chord, concrete slab, and the adjacent exterior

column (Column 144). 3-D quadratic finite strain beam elements were used.

• Exterior and interior truss seats and the gusset plate at the exterior end. Break elements were

used to model failures of these comiections.

• Spandrel studs, studs on the strap anchor, and knuckles. Break elements were used to model

failures of these connections.

Materials: Temperature-dependent elastic, plastic, and creep properties were included in steel members

except for columns and spandrels. The Hjelm plasticity model was used for the solid elements of the concrete slab that allowed different "yield strengths" in tension and compression.

Boundary Conditions: The entire top chord of the truss was restrained against the movement transverse to the truss axis. The bottom chord was restrained against the movement transverse to the truss axis at four

bridging truss locations. The two edges of the concrete slab parallel to the truss were restrained against

rotations about the tmss axis and the vertical axis, but were free in the translation along the truss axis. The interior tmss seat was fixed in all directions. The exterior truss seat was attached to the spandrel.

The truss was pinned at both exterior and interior truss seats. The interior end of the slab was fixed in the

vertical direction. In the truss axis direction at the interior end of slab, break elements were implemented

to represent temperature-dependent tensile capacities of steel reinforcement.

Loads: The loading on the truss model consisted of dead load and 13.75 psf of live load (equal to 25 percent of design live load for the WTC towers) and temperature time-histories for all truss components including the truss seats and concrete slab. Themial loads were assumed for exercising the

truss model. The temperature was ramped from 20 °C to 700 °C in steel members, from 20 °C to 700 °C

at the bottom of the slab, and from 20 °C to 300 °C at the top of the slab for the period from 0 min to 30 min; thereafter, the temperatures were linearly increased by an additional 200 °C at 40 min. A linear

temperature gradient through the thickness of the slab was assumed. Temperature was not applied to the

columns and spandrel.

Summary of Results: Key structural response of the truss model to "assumed temperature conditions" can

be summarized as follows:

• The stud on the spandrel and studs on the strap anchor failed in shear below 275 °C.

• The first knuckle from the interior end failed in vertical tension at around 100 °C.

• Top chords yielded above 300 °C due to the difference in coefficients of thermal expansion of

steel and concrete.

xxxvni NISTNCSTAR 1-6C, WTC Investigation
Executive Summary

• The floor sagged into a catenary shape as four compression diagonals buckled due to high

axial compressive force at 565 °C.

• The interior truss seat bolts sheared off, and the second and third knuckles from the interior end failed in the horizontal shear at 566 °C.

• The gusset plate fractured, and the exterior truss seat bolts sheared off at around 680 °C.

• The truss walked off the exterior truss seat at 730 °C.

Simplified Tmss Model: The truss model was modified for use in the full floor subsystem model to enhance computational efficiency. Characteristics captured by the simplified truss model were: (1) total horizontal reaction force under the thermal loading and (2) vertical deflection under the thennal loading.

The simplified truss model had the following features:

• Double primary truss was combined into a single truss. Areas of truss members were

doubled.

• The top and bottom chords and diagonals were modeled by 3-D linear finite strain beam

elements. Only one element was used for a member between two panel points.

• Break elements were used to model the following failure modes: (a) seat bolt shear-off, (b)

gusset plate fracture, (c) truss walk-off, (d) web diagonal buckling/resistance weld failure, (e)

failure of spandrel studs and studs on strap anchors, and (f) weld failure between strap

anchors and top chords. Knuckles were not modeled by break elements.

• Temperature-dependent elastic and plastic material properties of steel were used.

• Creep in steel was included in the simplified truss model; however, it was not included when

the simplified truss model was incorporated in the full floor model because of convergence

problems inherent to 3-D linear finite strain beam elements.

• The concrete slab was modeled by 4-node finite strain shell elements with a temperaturedependent bilinear material model that had the same yield strength in both tension and

compression. The yield strength was set to the compressive strength.

E.2.4 Full Floor Analysis

The full floor models were developed and analyzed using ANSYS to identify the most likely failure modes and the fire-induced damage to be incorporated in the global model along with impact damage and

to modify the floors in the global models to enhance computational efficiency.

Failure Modes: Possible failure modes of the floor subsystem were identified as follows:

• Sagging ofthe Floor System: Floor sagging caused by loss of stiffness, plastic bending, or buckling of web diagonal members resulted in tension in the floor subsystem, tension in the

connections to the exterior walls, and lateral forces (pull-in forces) on columns.

• Loss ofSupport: Loss of a truss support could be caused by (1) vertical shear load due to debris and/or impact load of the dropping floor above, (2) reduced resistance of truss seats under elevated temperatures, (3) tension acting on truss seats caused by floor sagging,

(4) cooling of a truss already shortened due to plastic deformation resulting from thermal

NISTNCSTAR 1-6C, WTC Investigation XXXIX
Executive Summary

loading, and (5) aircraft impact. Loss of support will reduce buckling strength of exterior

columns.

Model Description: The base floor model developed was for Floor 96 of WTC 1 with columns extending

from Floor 95 to Floor 97. The full floor model included the following structural members:

• Both exterior and core columns extending from one floor below to one floor above, modeled

by 3-D quadratic finite strain beam elements.

• Spandrels of the floor of interest, modeled by four-node finite strain shell elements (eight

elements between two columns and four elements along the height), which were tied to exterior columns by rigid beam elements.

• Floor slab was modeled by four-node finite strain shell elements with four layers tlirough the

thickness.

• Floor trusses including primary and bridging trusses. Two primary trusses supported by the same coluinn were combined into a single truss. Truss members (top and bottom chords and

web diagonals) were modeled by 3-D linear finite strain beam elements.

• Strap anchors, modeled by 3-D linear finite strain beam elements.

• Core beams, modeled by 3-D linear finite strain beam elements. They were placed at their

centroids and were connected to the slab by rigid beam elements.

• Deck support angles, modeled by 3-D linear finite strain beam elements.

Break elements were incorporated into the model to represent: 1) buckling of web diagonals, 2) gusset

plate fractvire, 3) truss seat bolt shear-off, 4) truss seat failure, 5) failure of connections between primary

and bridging trusses, 6) failure of connections between primary long-span and transfer trusses, 7) failure

of studs connecting the slab and the spandrel, and 8) failure of welds between strap anchors and top

chords of primary trusses. Break elements were not used for representing knuckle failure as the truss analysis found that buckling of web diagonal members preceded knuckle failures. The concrete slab was

always attached to primary trusses at knuckle locations in the full floor model.

Subsequent to the initial thermal response analysis, the following members were removed from the model

to enhance computational efficiency: 1 ) deck support angles, 2) bridging trusses outside of the two-way

zones, 3) spandrel studs connecting the slab and the spandrel, and 4) strap anchors. These members were

found to fail in the early stage of thermal loading, caused the analysis to slow down due to the large

residual nonlinearities in the subsequent stages of analysis. Deck support angles and bridging trusses buckled between primary trusses due to thermal expansion. Most spandrel studs and welds between strap

anchors and truss top chords failed due to lateral shear force in the plane of slab caused by the difference

in the thermal expansion between the floor and the exterior wall in the direction transverse to the truss

axis. As a result of the removal of strap anchors and spandrel studs, the only connections between the

exterior wall and the floor were gusset plates and exterior truss seats in the full floor models.

Materials: Temperature-dependent elastic and plastic material properties of steel provided by NIST were

assigned to each structural member according to the PANYNJ drawings. It was found that creep in 3-D

linear/quadratic finite strain beam elements would cause convergence problems when those elements

experience thermally-induced buckling. Therefore, creep could not be included in the full floor models.

For the concrete slab, a bilinear stress-strain relationship with a yield point at its compressive strength was used, where the yield strength was the same in both tension and compression.

xl NISTNCSTAR 1-6C, WTC Investigation
Executive Summary

Impact Damage: Elements corresponding to structural members that sustained severe structural damage

were removed from the model. Based on the aircraft impact analysis, NIST identified two sets of

structural and thermal insulation impact damage for each floor. These impact cases were designated as "Case A, impact damage condition" and "Case Bi impact damage condition" for WTC 1, and "Case Cj

impact damage condition" and "Case Dj impact damage condition" for WTC 2.

Boundary Conditions: Both core and exterior columns were fixed in the vertical direction at the bottom.

When the column below the floor was severed by aircraft impact, the top of the column above the floor was supported in the vertical direction. Core columns were free in the horizontal directions and fixed for

all rotations at the top and bottom ends. Exterior columns were fixed for translation perpendicular to the

face of building and from rotating about the axis parallel to the face of the building at the top and bottom.

They were also fixed in torsion at the top and bottom.

Loads: The full floor model was first analyzed for dead load and 25 percent of design live load of the

WTC towers, and then temperature time histories representative of the WTC fire conditions were applied.

Vertical loads to columns were not applied. NIST provided temperatures of structural components from

reconstructed fires in the WTC towers based on the impact damage conditions; therefore, the impact

damage condition and the temperature condition had one-to-one correspondence. Temperature cases

pro\ ided were "Case A, temperature condition" and "Case B, temperature condition" for WTC 1, and

"Case C, temperature condition" and "Case D, temperature condition" for WTC 2. Temperature data sets were provided at 10 min time intervals up to 100 min for WTC 1 and up to 60 min for WTC 2 for each

temperature condition.

Summary of Results: The behaviors of the floor subsystem found in the full floor models subjected to impact damage and fire conditions can be summarized as follows:

• Bridging trusses subjected to elevated temperatures buckled between primary trusses.

• When significant differences in the thermal expansion occurred between the floors and the

exterior wall in the direction transverse to the primary trusses, spandrel studs, strap anchors,

gusset plates, and seat bolts failed due to lateral shear force.

• Floor sagged as the web diagonals of floor trusses buckled in the heated area where the

thermal insulation was damaged.

• The floors were disconnected from the exterior wall in some areas due to failure of exterior

truss seats.

Pull-in forces were expected to develop whenever the floor sagged. Although the floor sagging was

captured by the full floor models, the pull-in force was not captured in most of the full floor model

analyses. To accurately calculate pull-in forces between the floor and the exterior coluinns in the full floor model, much more detailed modeling was required. Such modeling included accurate boundary

conditions on columns, creep in steel, friction at the truss seats, and accurate evaluation of failure of strap

anchors and stud, and concrete cracking and spalling. In addition, temperatures of structural members

might be low due to conservative assumption of limiting the insulation damage to debris abrasion and

neglecting the effect of aircraft shock and vibration.

Floor Subsystem in Global Models: To enhance computational efficiency, floors in the global models

were modeled by shell elements to have the following functions: 1) diaphragm action and 2) transfer of

the load from the core to the exterior wall system by a membrane action. Since the floors modeled by

shell elements cannot capture key failure modes under elevated temperatures, including sagging of floors

NISTNCSTAR 1-6C, WTC Investigation xli
Executive Summary

and disconnection of floors from the exterior wall, their effects need to be implemented in the global

model as fire-induced damage at appropriate points in time.

E.3 EXTERIOR WALL SUBSYSTEM

The exterior wall subsystem was a nine-column (three-panel) wide by nine-story (three-panel) high

section of WTC 1 between Floor 91 and Floor 100 and Column 150 and Column 158 as shown Fig. E-5.

This area, typical of the exterior walls of the towers, connected to a part of the floor system near the comer.

Each face of the towers' exterior wall consisted of fifty -nine 14 in. square box columns spaced at 3 ft 4 in. on center, with 52 in. deep spandrel plates at each floor level. The exterior wall was constructed with

shop-welded prefabricated panels, each consisting of three columns and three spandrel beams, 13 ft 4 in. wide by 36 ft high. Except at mechanical floors and the base and top of the structure, vertical splices

(column splices) in prefabricated panels were staggered such that within any story, every third prefabricated panel had a column splice (see Fig. E-5). Exterior column sphces at the upper stories typically consisted of four 7/8 in. diameter ASTM A325 bolts fastened through the welded butt plates at the tops and bottoms of adjoining columns. Special prefabricated panels existed for the mechanical floors where no stagger existed at Floors 7, 41, 75, and 108. At these mechanical floors, the column sphce

detail included supplemental field welding in addition to the bolted connection. Horizontal (spandrel-tospandrel) connections between prefabricated panels were all field-bolted using splice plates. Comer

panels that connected the orthogonal walls at comers were two-story tall (24 ft) and consisted of two

columns, two spandrel plates, and a third column midway between the two columns on altemate floors.

Various grades of steel, having yield strengths ranging between 42 ksi and 100 ksi, were specified for the

exterior column and spandrel plates. Column plate thickness also varied, both vertically and around the

building perimeter. Column plate thickness was as thin as 1/4 in. at the upper stories and increased

toward the base of the building.

E.3.1 Single Column Analysis

A single exterior column model was developed to examine column behavior under compression at different temperatures. The model included a one story high portion of Column 151 extending from

Floor 95 to Floor 96 and portions of spandrels at Floor 95 and Floor 96. Four-node finite strain shell elements were used to model the plates of the column and the spandrels. Nodes of column plates at the

top and the bottom of the model were rigidly tied to the center of gravity of the column cross section. The

column was pinned at the bottom and fixed in the two horizontal directions at the top. Increments of axial

displacement were applied at the top of the model at room temperature and 700 °C. The calculated capacity of the columns spanning a single floor occurred after local buckling of plates and

the subsequent kinking of the cross section at 1,030 kip at room temperature, well below the inelastic buckling strength of the column, and 270 kip for 700 °C. Since the compressive force demand on this particular column was estimated at 175 kip, the compressive strength of the column is greater than the

demand even at 700 °C. The column underwent kink-type buckling at room temperature, and the loadcarrying capacity in the post-buckling regime decreased rapidly; however, it decreased much more

gradually at 700 °C.

xlii NISTNCSTAR 1-60, WTC Investigation
Executive Summary

Axial load-displacement behaviors of two and three-story single column models were also examined. As

the unsupported length became longer and temperature increased, local buckling of plates and the

resuUing kinking of the cross section did not occur, and the negative slope of the axial load-deflection

curv e in the post-buckling regime became less steep.

E.3.2 Column Splices

Failure Modes: Failure modes identified for column splices were: (1) failure of bolts in tension, (2) failure of bolts in shear. (3) bending failure controlled by tension in bolts. Tension capacity was calculated as the ultimate tension capacity of four bolts. Shear capacity was calculated as the addition of bolt shear

capacity and splice friction. The ultimate moment capacity was obtained prior to failure of two bolts with some capacity remaining on other two bolts. Column Splice Model for Exterior Wall Model: Two 3-D quadratic finite strain beam elements for each

of the four bolts, four pairs of 3-D node-to-node contact elements at the faying (contact) surfaces, and

rigid beam elements, modeled by 3-D elastic beam elements, comiecting the tops of the bolts to the contact elements, were used to model the column splice. Break elements were used to model the fracture of the column splice bolts based on data from bolt tests provided by NIST and on shear failure of the

splice. A coefficient of friction of 0.35 was used for the contact elements. The 7/8 in. diameter column

splice bolts were preloaded to 36.05 kip at 20°C.

E.3.3 Spandrel Splices

Failure Modes: Failure modes identified for spandrel splices were: (1) bolt shear, (2) tearing of the

spandrel plate, and (3) tearing of the splice plates at the bolt holes. Capacities of these failure modes at different temperamres were estimated by hand calculations.

Spandrel Splice Model for Exterior Wall Model: Break elements were used to model the spandrel splice

connections in the model. At each splice location, eleven break elements were used. Nodal couples were

used to model the spandrel splice connections on the boundaries of the model.

NISTNCSTAR 1-6C, WTC Investigation xliii
Executive Summary

inininmininininin

T-T-r— r-T-T-T-T-T— _l_!_l_i_S_f_i_!_l ooooooooo ooooooooo

Floor 99

Floor 98

Floor 97

Floor 96

Floor 95

Floor 94

Floor 93

Floor 92

12 ft

Floor 91

I

I

1

I

I

I

I

I

I

T

40 in.

Spandrel splice

Column splice

Prefabricated panel

~|~52 in.

11 in.

V

13.5 in.

<

10ft

14 in.

Section A-A

40 in.

Figure E-5. Exterior wall subsystem.

E.3.4 Exterior Wall Analysis

Failure Modes: The exterior wall subsystem model captured the following failure modes:

• Inelastic buckling of columns from large lateral deformations,

• Inelastic buckling of columns from loss of support at floor truss seats and diagonal straps,

• Failure of column splice bolts, and

• Failure of spandrel sphce bohs or tearing of spandrel or splice plates at bolt holes.

xliv NISTNCSTAR 1-6C, WTC Investigation
Executive Summary

The model did not capture the local buckling of the column plates and the resulting kinking of the cross

section. This was justified because the exterior walls were observed to have bowed inward over more than

three floors prior to the collapse, and temperatures of the columns of these walls were high. In these

cases, the kink-t>'pe buckling of columns did not occur. Model Description: BEAM 189 elements modeled the columns. Above and below spandrels, 3-D

quadratic finite strain beam elements modeled the complete cross sections of the columns. Four-node

finite strain shell elements modeled the spandrels. Rigid beam elements connected nodes on the axis of

the columns to nodes located in the mid-plane of the spandrels.

Materials: Temperature-dependent elastic and plastic material properties of steel provided by NIST were

assigned to each structural member according to the drawings. Creep in steel was included unless the

analysis was a displacement-controlled analysis.

Boundary Conditions: The bottoms of all columns in the model were restrained in the vertical direction.

The top and the bottom of all columns in the model were restrained in the direction nonnal to the wall. In addition, the bottom of central column was restrained in the plane of the wall. Symmetry boundary

conditions were imposed on the spandrels at the boundaries of the model, except that the spandrels were

free to expand in the plane of the wall. Motion out of the plane of the wall was restrained at all floor truss seats and straps. In several analyses, such restraints were removed at two or three floors (either Floors 95

and 96 or Floors 95, 96, and 97) to investigate the effect of floor sagging and floor/wall disconnection on

stability of the exterior wall system.

Loads: The loads on the model were applied sequentially in the following order:

• Self weight of the exterior wall components,

• Column splice bolt preload,

• Dead load of the floor system, including 8 psf superimposed dead load,

• 25 percent of WTC floor design live loads,

• Temperatures of fire scenarios provided by NIST, and

• Transverse pull loading from sagging trusses or additional vertical deflection from a potential

redistribution of forces to this portion of the exterior wall. To represent a range of thermal conditions expected in the WTC towers, NIST provided five thermal load

conditions: D, DBARE, E. El 19. and F. These load conditions differed in fire behavior, intensity,

location in the towers, and time. Thermal load DBARE assumed steel without insulation. Thermal load

El 19 corresponded to the standard ASTM El 19 fire load.

Summar\' of Results: The response of the exterior wall model subjected to thermal loads can be

summarized as follows:

• Large inelastic buckling of spandrels occurred at elevated temperatures.

• Although partial separations of the spandrel splices occurred at elevated temperatures,

complete separation did not occur.

• Instability of the exterior wall subsystem did not occur at elevated temperatures when the

wall was supported laterally at every floor. Instability of the exterior wall subsystem

occurred when at least three floors were unbraced and the exterior wall subsystem was

subjected to additional vertical load or pull-in force.

NISTNCSTAR 1-6C, WTC Investigation xlv
Executive Summary

• All column splices remained closed, except near the points of instability of the exterior wall

with tliree floors unbraced and subjected to additional vertical load or pull-in force where

calculations showed opening and sliding of the splice with no bolt fracture.

Exterior Wall Subsystem in Global Models: The analyses of the exterior wall model support the following

conclusions for modeling the towers:

1. Large inelastic deformations and buckling of the spandrels do not significantly affect the

stability of the exterior columns and need not be accurately modeled in the global models.

2. Partial separations of the spandrel splices do not significantly affect the stability of the

exterior columns and need not be accurately modeled in the global models.

3. Exterior column splices can be expected to fail by sliding or opening at elevated temperatures

when subjected to increased vertical loading or pull-in forces. Since complete failure was not found before the exterior wall became unstable, column splice failure may not be modeled in the global models to enhance computational efficiency.

E.4 RECOMMENDED MODELING DETAILS FOR SUBSYSTEMS IN GLOBAL

MODELS

Based on the results of finite-element analyses performed on components, connections, and subsystems,

the following recommendations can be made for modeling of the subsystems in the global models to enhance numerical efficiency.

Floor Subsystem

Floors in the global model may be modeled by shell elements, which have their membrane stiffness equal

to that of the full floor system. Floors in the global model function as diaphragms and transfer load

between the exterior wall system and the core. The global model cannot be constructed with the same level of detail in all floors subjected to thennal

loading as the full floor model developed here. To enhance computational efficiency, the pull-in forces

and disconnections of floors from the exterior walls may be implemented in the global models as "fire- induced damage" at appropriate times. Since the full floor models could not be used to calculate

accurately the pull-in forces at floor/wall connections, the fire-induced damage obtained from the full floor model analyses needs to be modified by the results of "actual observations" obtained from the

examination of photographs and videos performed by NIST (NIST NCSTAR 1-5 A).

Exterior Wall Subsystem

The exterior and interior columns must be modeled with fidelity of their inelastic buckling behavior. To

capture the premature buckling of the single span exterior columns at low temperatures, which occurs at the onset of plate buckling and results in kinking of the cross section, a fine mesh is needed. However,

observations of photographs and videos show that bowing is extended over several floors and column

temperatures are not low. Therefore, kink-type buckling of the exterior columns may be neglected.

Exterior column splices need not be modeled in the global models.

Spandrels can be modeled by beam elements capable of resisting shear and bending moment. The

spandrel sphces need not be modeled in the global analyses.

xlvi NIST NCSTAR 1-6C, WTC Investigation
Chapter 1 Introduction

1.1 PURPOSE

Simpson Gumpertz & Heger Inc. (SGH) developed finite-element models of the components,

connections, and subsystems of the World Trade Center (WTC) towers to study their structural performance in the fire environment that followed the aircraft impact to the towers. The results of this study were used to develop global models that ran efficiently and captured the important failure modes

and sequential failures of components and subsystems and to determine the probable sequence of

structural responses that let to the global collapse initiation. SGH performed this study as part of Project 6 of the investigation on the WTC disaster by the National

Institute of Standards and Technology (NIST). This report constitutes the SGH's report on Task 1 of the

SGH contract with NIST and Part 1 of the SGH two-part report. The Task 2 and 3 report deals with the

global analysis of the WTC towers (NIST NCSTAR 1-6D').

1.2 SCOPE OF WORK

SGH in Task 1 performed the following:

• Developed and validated ANSYS models of the full floor and exterior wall subsystems.

• Evaluated structural responses of components, connections, and subsystems to service loads

due to gravity (dead and live loads) and elevated temperatures.

• Identified the likely failure modes and failure sequences of components, connections, and

subsystems.

• Identified modeling details of the floor and exterior wall subsystems in the global models of

the WTC towers.

The analyses performed as part of this Task 1 report used the nominal dimensions and design details shown on the PANYNJ drawings'. Material properties were based on information provided from the

NIST Project 3 study (NIST NCSTAR 1-3, NIST NCSTAR I-3D).

1 .3 REPORT ORGANIZATION

This report consists of eight chapters:

• Chapter 1 serves as an introducfion to this report and describes purpose and scope of this study.

This reference is to one of the companion documents from this Investigation. A list of these documents appears in the Preface

to this report. The technical data required to conduct the analyses of the WTC towers reported herein were obtained from drawings that were

provided by the Port Authority of New York and New Jersey (PANYNJ) and their contractors.

NIST NCSTAR 1-6C. WTC Investigation 1
Chapter 2 introduces a floor subsystem and an exterior wall subsystem of the WTC towers

and provides descriptions of their structural details.

Chapter 3 summarizes temperature-dependent material properties of steel and concrete used

in this study.

Chapter 4 describes a conversion process from SAP2000 reference models to ANSYS models

and presents validation studies of the converted ANSYS models.

Chapter 5 presents results from a study on the full floor subsystem.

Chapter 6 presents results from a study on the exterior wall subsystem.

Chapter 7 summarizes recommendations for modeling details of the full floor subsystem and

the exterior wall subsystem in the global models.

Chapter 8 provides a list of references.

NISTNCSTAR 1-6C, WTC Investigation
Chapter 2

Description of Subsystem Structures

The finite-element models of the full floor subsystem and the exterior wall subsystem of the World Trade

Center (WTC) towers were developed to calculate the structural response of these subsystems to impact

damage and to the fire enviromnents that followed the aircraft impact. The ftill floor subsystem is a model of Floor 96 of WTC 1 . The model is believed to be t}'pical of the upper floors in both towers. The

exterior wall subsystem is a nine-column (three-panel) wide by nine-story (three-panel) high section of

WTC 1 between Floor 91 and Floor 100 and Column 150 and Column 158. This area is typical of the exterior walls of the towers and connects to a part of the floor system near the comer with different types

of trusses.

2.1 FULL FLOOR SUBSYSTEM DESCRIPTION

Floor 96 of WTC 1 was identified as an office floor with typical floor construction and loading; therefore,

it was selected as the basis for modeling floor response. The full floor subsystem included office area and

core area floor framing, as well as core and exterior columns extending to floors immediately above and

below this floor. The floor system in the office area consisted of lightweight concrete slab supported by

steel floor trusses. Steel trusses spanned nominally 60 ft in the long-span area and 36 ft in the short-span

area between exterior walls and the central core. Typically, a pair of primary trusses (double truss) was

supported at odd-numbered columns at 6 ft 8 in. on center.

Each of these primary trusses consisted of top and bottom chords fabricated from double steel angles and

web diagonals fabricated from round bars (see Fig. 2-1). Web diagonals extended 3 in. above the top

chord at the panel points into the concrete slab to form a knuckle and to provide shear transfer between

the truss and the concrete slab (see Fig. 2-1).

Hand calculations and finite-element analyses of components of the full floor subsystem and their connections were performed under gravity loads and fire-induced temperature time-histories to capture

the different failure modes and loads at failure. Then the results of these calculations and analyses were

used to develop the full floor subsystem model.

The top chords of a pair of trusses were supported at the central core by an interior truss seat (Fig. 2-1)

welded to steel channels that ran continuously around the core floor area. Each pair of trusses was

fastened to a horizontal plate of the interior truss seat by two 5/8 in. bolts (one bolt in each truss) in

1 3/4 in. long slotted holes. At the exterior wall, each pair of trusses was supported by an exterior truss seat (Fig. 2-1), which fastened to a seat angle with two 5/8 in. diameter bolts in 2 in. long slotted holes. A pair of stand-off plates welded the seat angle to the spandrel. In addition, a gusset plate welded to the

spandrel and to the truss top chord tied the truss to the supporting column, and a pair of diagonal strap

anchors, welded to the top chords and to the adjacent columns, tied these columns to the primary trusses.

Figure 2-2 shows a floor plan of Floor 96 of WTC 1. Primary trusses were interconnected by a transverse system of bridging trusses and deck support angles. These bridging trusses were of similar construction

to the primary trusses, except the knuckles did not project above the top chords. The top chord of the

bridging trusses sat 1 1/2 in. below the top chord of the primary trusses and provided support for the 4 in. thick lightweight concrete slab on the 1 1/2 in., 22 gauge steel deck with 2 in. wide at the top, 1.25 in.

NISTNCSTAR 1-6C, WTC Investigation 3
Chapter 2

wide at the bottom, and 1.5 in. high flutes at 6.8 in. on center running parallel to the primary trusses. At

each comer of the building core, a 36 ft long transfer truss extended out from the comer core coluinn to the exterior wall and supported the 60 ft long primary tmsses. The floor in the core consisted of a 4.5 in. thick lightweight concrete slab supported by wide flange girders and beams connected to the core columns with bolted connections. Reinforcement between the core area floor and the office area floor

(#3 bars at 10 in. at the top and #4 bars at 12 in. at the bottom) provided continuity between the two areas and restrained the truss from walking off the interior seat.

Primary

double truss

Figure 2-1. Mock up of office floor framing system (Photograph from about 1967

provided by Laclede Steel Co.).

4 NISTNCSTAR 1-6C, WTC Investigation
Description of Subsystem Structures

Exterior column

number

Exterior column

Diagonal strap

anchor

Transfer truss

-101 103 106 109 112 115 118 121 124 127 130

Short-span

primary

double truss

Ittl 100 IDS 109 1U 115 118 1?l 1« 1Z7 1» i..i.J..l..i,.i.,i..i.J

'501

60t 602 603 B04 6 S 806 607

TM3 704 7 S ^

133 136 13e 142 I4i 148 tSI ISA 1S7 1SS

503 S04 S 5 SOe 607

903 804 DOS

903 903 904 BOS 906

1002 1003 1004 10O5 1006

707

806

i'*i"n T i l f i l l

708'

807'

• 90811 907

1?P 10O8. m

Long-span

primary

double truss

Bridging truss

Core column

and core column number

N

I

Core area

» 357 3M XI Mt 346 33e 3» 333 XD m 3>t 321 318 31S 312 3I» 306 30) 3D!

Figure 2-2. Floor plan of Floor 96 of WTC 1

NISTNCSTAR 1-6C, WTC Investigation 5
Chapter 2

2.2 EXTERIOR WALL SUBSYSTEM DESCRIPTION

Each exterior wall of the towers consisted of fifty-nine 14 in. square box columns spaced at 3 ft 4 in. on

center, with 52 in. deep spandrel plates at each floor level. The exterior wall was constructed with shopwelded prefabricated panels, each consisting of three coluinns and three spandrel beams, 13 ft 4 in. wide

by 36 ft high. Except at mechanical floors and the base and top of the structure, vertical splices (column

splices) in prefabricated panels were staggered such that within any story, every third prefabricated panel

had a column splice (see Fig. 2-3). Exterior column splices at the upper stories typically consisted of four

7/8 in. diameter ASTM A325 bolts fastened through the welded butt plates at the tops and bottoms of

adjoining columns. Special prefabricated panels existed for the mechanical floors where no stagger

existed at Floors 7, 41, 75, and 108. At these mechanical floors, the column splice detail included

supplemental field welding in addition to the bolted coimection. Horizontal (spandrel-to-spandrel)

connections between prefabricated panels were all field-bolted using splice plates. Comer panels that connected the orthogonal walls at comers were two-story tall (24 ft) and consisted of two columns, two

spandrel plates, and a third column midway between the two columns on altemate floors.

Various grades of steel, having yield strengths ranging between 42 ksi and 100 ksi, were specified for the

exterior column and spandrel plates. However, fewer grades were actually used than specified by

supplying a single grade steel for the 3 highest specified yield strengths. Column plate thickness also

varied, both vertically and around the building perimeter. Column plate thickness was as thin as 1/4 in. at the upper stories and increased toward the base of the building. The specified plate thickness and material

yield strength for each column differed between the two towers primarily due to the 90-degree change in the building orientation between the two towers and computed wind loads (NIST NCSTAR 1-2).

The model of the exterior wall subsystem was a nine-column (three-panel) wide by nine-story (threepanel) high section of WTC 1 between Floor 91 and Floor 100 and Column 150 and Column 158 as shown Fig. 2-3. This area, typical of the exterior walls of the towers, connected to a part of the floor

system near the comer. (Column 159 is at the comer of the north face of WTC 1, see Fig. 2-3). Using

this model, the stmctural behavior and failure modes of the exterior wall system were evaluated in the fire environment.

6 NIST NCSTAR 1-6C, WTC Investigation
Description of Subsystem Structures

Prefabricated panel Spandrel splice

Floor

Floor

Floor

I

f

I

I

I

I

I

I

I

I

I

I

I

]— Column

splice

Floor _

12ft

Floor - I

I

10ft

I

I

I

I f

r

I

40 in. \

I

I

I

I ]"^52 in.

40 in.

Figure 2-3. Exterior wall construction with prefabricated wall panels.

2.3 LOADS

The subsystems and components were analyzed for dead (D), live (L), and thermal (Ta) loads. The dead

load consisted of structural weight and superimposed dead loads. The superimposed dead load and design

live load were defined in the World Trade Center Design Criteria (LERA 2003). The superimposed dead

loads for floors outside the core consisted of the weights of ceiling, mechanical and electrical equipment,

passive fire protection (also referred to as thermal insulation or fireproofing), and floor finish, and were

estimated at 8 psf Twenty five (25) percent of the design live load was selected as a reasonable

approximation of the load that likely existed at the time of the collapse. (For example, 25 percent of the

design live load resulted in a load of 13.75 psf for the long-span trusses in the two way zone of Floor 96

NISTNCSTAR 1-6C, WTC Investigation 7
Chapter 2

with 55 psf design live load.) The service dead and live loads were applied first, followed by the thermal

loads.

The dead and live loads were defined as weights, so that during the collapse process, the gravity loads

remained acting on the structure. The weight of debris from the plane provided by Project 2 (NIST

NCSTAR 1-2) was found to be negligible relative to the dead and sei-vice live loads and was not included

in the analysis.

The thermal loads, Tg, were temperature time histories for all structural members provided by Project 5 (NIST NCSTAR 1-5, NIST NCSTAR 1-5G).

For analysis of some of the components, discrete values of temperature or temperature distributions were

linearly ramped from 20 °C to 700 °C (or to a temperature below 700 °C that results in the failure of the

component) over 30 min. Failure modes of the components were evaluated at room temperature and at different elevated temperatures, as failure modes and failure loads may change with increasing

temperature.

Although wind may have had a minor role in the collapse of the towers, all analyses performed in this study did not include wind load effects.

8 NIST NCSTAR 1-6C, WTC Investigation
Chapter 3

Materials

The mechanical properties of both steel and concrete are affected significantly by temperature. In the

following sections, the material properties used in this study are specified as a function of temperature.

For finite element analysis (FEA) of components, subsystems, and global models of the World Trade

Center (WTC) towers, a material properties catalog was developed. Each material model was identified

with a number in ANSYS; steels were Material ID 1 through Material ID 29, and concretes were Material

ID 51 through Material ID 83. The details of different materials are discussed for concrete and steel separately in this chapter.

3.1 CONCRETE

Two t>'pes of concrete were generally used for the flooring inside the towers: lightweight concrete and

normal weight concrete. Thermal properties of normal weight concrete depend on the type of aggregate.

Petrographic inspection by Simpson Gumpertz & Heger Inc. of two samples of concrete taken from the

debris at NIST showed siliceous sand. Because the source of coarse and fine aggregates for a construction site is usually the same, available data for siliceous aggregates were used.

3.1.1 Concrete Properties

The unit weight of the lighrv\'eight concrete was specified at 100 pcf by the WTC Design Criteria (LERA

2003); however, 110 pcf was used in the analysis based on the density of the two concrete samples

examined by SGH. The unit weight of the normal weight concrete was specified at 150 pcf by the

WTC Design Criteria (LERA 2003).

Poisson's ratio, v^. , of 0.17 was used for both normal weight and lightweight concrete at all temperatures.

The specified concrete strength was 3,000 psi for the lightweight concrete, and either 3,000 psi or 4.000 psi for the normal weight concrete, as shown on Drawing Book 8, Sheet AB 1-2.1 (SHCR 1973).

The actual strength, , of in-place concrete at room temperature was calculated from the specified

strength. . as follows:

L=f:-FrF,-F, (1)

where the factor Fi = the ratio of the average strength of 28-day cylinders to specified strength, F: = the

ratio of in-situ 28-day strength to 28-day cylinder strength, and F3 = factor that accounts for the change in concrete strength with age. By using F, = 1.25 and F: ^ 0.95 (Bartlett and MacGregor 1996) and = 1.16, based on the formula

specified in Section 2.2.1 of American Concrete Institute (ACI) 209 for the change of concrete strength

with age, the mean of the ratio of actual strength of in-place concrete to the specified concrete strength was determined to be / /J = 1.38. Based on this mean value, the actual strengths of in-place concretes

are = 5,500 psi for the specified 4,000 psi normal weight concrete, 4,100 psi for the specified

3,000 psi normal weight concrete, and 4,100 psi for the specified 3,000 psi lightweight concrete.

NISTNCSTAR 1-6C, WTC Investigation 9
Chapter 3

Temperature-dependent properties of concrete used in this study were modulus of elasticity, instantaneous

coefficient of thermal expansion, compressive strength, and tensile strength.

Modulus of elasticity at room temperature was evaluated by the following fonnula:

E^iRT) = 33r:'JL (2)

For the compressive strength, the actual strength, , was used as the compressive strength at room

temperature. The tensile strength at room temperature was evaluated by:

(3)

The effects of elevated temperature on concrete properties are based on the work of Phan (1996) as shown

in Fig. 3-1.

3.1.2 Concrete Stress-Strain Relationships

The compressive stress-strain relationship for concrete, formulas expressed by Seanz (1964), is given by

\ + a

f \ ( \

1 £ + b

£ + C

(4)

Where,

-1

c =

1 085

Z) = 1 - 2c , a — c + K^, - 2,

K^^\A\ , and ^.-1=^.^

In tension, stress increases linearly up to the tensile strength. When concrete is strained in tension beyond

its strength, it softens, and the stress drops. However, the descending branch of stress-strain relationship

caused significant numerical problems which were avoided by assuming, with little error, that concrete becomes plastic in tension. The assumption of concrete plasticity after the onset of micro-cracking is valid for reinforced concrete with a reinforcement ratio of about a ratio of the tensile strength of concrete

to the yield strength of reinforcement, which is 0.46 percent. The reinforcement ratio in the typical concrete slab in the WTC towers was 0.21 percent in the primary truss direction and 0.74 percent in the

direction transverse to the primary trusses. Although the reinforcement ration in the truss direction was

smaller than 0.46 percent, the resulting error was not significant. Figure 3-2 shows stress-strain curves of

concrete with 3,000 psi specified compressive strength at room and elevated temperatures.

10 NISTNCSTAR 1-6C, WTC Investigation
Materials

5 10

200 400 600 Temperature (°C) Normal-weight (3000 psi) Normal-weight (4000 psi) Lightweight

(a) Modulus of elasticity

1000 400 600 000 Temperature (°C) Normal-weight (3000 psi or 4000 psi) Lightweight

(b) Instantaneous coefficient of thermal expansion

6000

400 600 Temperature ("C) Normal-weight (3000 psi) Normal-weight (4000 psi) Lightweight

(c) Compressive strength

1000

400

^ 300

£ 200

100 3000 psi normal-weight

and lightweight

0 200 400 600 Temperature (°C) Normal-weight (3000 psi)

- Normal-weight (4000 psi) Lightweight

(d) Tensile strength

800 lOOC

Figure 3-1. Properties of concrete that vary with temperature.

NISTNCSTAR 1-6C, WTC Investigation 11
Chapter 3

-0.015 -0.01 -0.005 0 -0.015 -Q.Ol "0.005 0

Strain (in/in) Strain (in/in) T-RT T-RT

T=300°C . ..„.,. T=300X

---- T=600°C T=600°C

(a) Normal-weight concrete (3,000 psi) (b) Lightweight concrete

Figure 3-2. Concrete stress-strain relationships at different temperatures.

For the knuckle model in LS-DYNA, solid concrete elements were used with Pseudo Tensor material

model (Livermore Software Technology Corporation 2003). The response mode II default concrete option was used. Properties of welded wire fabric were smeared into the concrete material properties,

assuming a steel reinforcement of 0.47 percent and a yield strength of wire of 70 ksi, where 0.47 percent

steel reinforcement was the average of the reinforcement in the two horizontal directions. Since material

properties cannot be defined as temperature-dependent properties in this model, different material types were specified for the lightweight concrete at 20 T, 150 T, 300 °C, 450 T, 600 T, and 750 °C (Material

IDs 51 through 56) with different stress-strain relationships.

The concrete floor slab in the truss model was modeled with eight-node solid elements (SOLID185) with

a material model that accounts for different behaviors in tension and compression. One such material

model in ANSYS is the Hjelm plasticity model with different yield properties in tension and compression.

A low "yield stress in tension" was used to simulate cracking of concrete. The Hjelm model uses the

Rankine maximum stress criterion in tension and the von Mises yield criterion in compression (ANSYS,

Inc. 2004). Concrete material models with the Hjekn model for the specified 3,000 psi normal weight

concrete, the specified 4,000 psi normal weight concrete, and the specified 3,000 psi lightweight concrete were assigned to Material ID 81, 82, and 83, respectively. To improve convergence in analysis, the

negative slope in the stress-strain relationship after cracking or crushing in compression was removed,

and the concrete was assumed to be plastic after cracking or crushing.

Isotropic hardening von Mises plasticity with a bilinear stress-strain relationship was used for the shell element modeling of the concrete slab in the full floor model. The model was elastic until the stress reached the compressive strength. It has the same yield strength in both tension and compression and,

thus, did not accurately represent the tensile softening of concrete. This model did have temperaturedependent material properties.

12 NISTNCSTAR 1-6C, WTC Investigation
Materials

3.1.3 Concrete Failure Criteria

The Mohr-Coulomb failure surface with end caps (a tensile cut-off stress and a compressive failure end

cap) was used in the Pseudo Tensor material model in the knuckle analysis (Livermore Software

Technology Corporation 2003). The cut-off stress for tensile failure was set as

^c.=l-7(/J^'^ (5)

3.2 STEEL

Steel types used in WTC 1 and WTC 2 are listed in Table 3-1 along with the actual yield and tensile strengths used in analysis. NIST examined the WTC steels in Project 3 and determined their material

properties (NIST NCSTAR 1-3). There were a number of steel suppliers and the multiple sources for

steel components of the same grade resulted in different strengths.

3.2.1 Steel Properties

Figure 3-3 shows mechanical properties of steel that are affected by elevated temperatures: (a) modulus

of elasticity, (b) Poisson's ratio, (c) yield strength reduction factor, (d) tensile strength reduction factor,

and (e) instantaneous coefficient of thermal expansion. All steel properties, except yield and tensile

strength reduction factors for bolt steels, are the same for all steels shown in Table 3-1.

3.2.2 Stress-Strain Relationship

Plasticity: Stress-strain relationships at room temperature were provided by Project 3. They were

constructed from mill reports, actual test data, and literature information using the Voce hardening law.

Stress-strain relationships at elevated temperatures, without consideration of creep, were obtained from

the power law:

cr = Rj,RrK{T)£cp (6)

where:

/:(r) = (yt4-A'0)exp^-0.5

( J \ ( J \ +

[1k\) [tkl] + kO

niT) = (n4-nO)exp\-0.5

tn\ +tnl + «0

The steel stress-strain relationships at different temperatures varied depending on the type of steel used in the construction of the towers. Values for Rj^ and R^ are given in Table 3-1, and parameters of

functions K{T) and n{T) , which were provided by Project 3, are given in Table 3-2. The stress-strain curve is linear with Young's modulus up to the "linearity limit." At the linearity limit, the linear stress- strain curve intersects the power law stress strain curve. (Stress at the linearity limit at elevated

temperature was not necessarily equal to the yield stress at the given temperature. The linearity limit was

required for ANSYS input.)

NIST NCSTAR 1-6C, WTC Investigation 13
Chapter 3

0 2(10 400 600 800 lOOO 0 200 400 600 800 1000 Temperature (°C) Temperature (°C) —— Construction Steel Construction Steel

Bolt Steel • Bolt Steel

(c) Yield strength reduction factor (d) Tensile strength reduction factor

1.710

0 200 400 600 800 1000 Temperature (°C)

(e) Instantaneous coefficient of thermal expansion

Figure 3-3. Properties for all steel types that vary with temperature.

14 NISTNCSTAR 1-6C, WTC Investigation
Materials

Table 3-1. Steel types used in WTC 1 and WTC 2.

Material ID Description (psi)

^uRT

(psi) Rc

1 All 36 ksi core box columns, plates, straps"' 36.720 64,470 1.086 0.857

All 36 ksi core WT. channels, and tubes 36 ksi large area and large inertia "rigid" beams in SAP2000 moder

37.000 63,450 1.069 0.954

Ji AW 42 ksi box columns (1<=0.75 in.) 51,400 79,200 1.070 0.884

4 All 42 ksi box columns (0.75 in. < t <= 1.5 in.) 47.000 74,800 1.010 0.884

5 A\] 42 ksi box columns (t > 1.5 in.) 42.600 70,400 0.951 0.880

6 42 ksi or 45 ksi Group 3 ^^T core columns 53.800 74.400 1 .005 0.977

7 42 ksi or 45 ksi Group 3 \\T core columns 49.000 71.040 0.960 0.954

8 42 ksi Group 4&5 \\T core columns 44.200 66.640 0.900 0.948

y 45 ksi Group 4&5 \VF core columns 47,800 71.074 0.960 0.939

10 .A.11 36 ksi Plates 1. 2. and 4 in perimeter columns 35.630 61,170 1.031 0.875

11 All (42. 45. or 46) ksi Plates 1 . 2. and 4 in. perimeter

columns

53.051 74,864 1.011 0.948

12 All 50 ksi Plates 1. 2. and 4 in. perimeter columns. All 50 ksi channels and plates^

53,991 75,618 1.021 0.978

13 All 55 ksi Plates 1. 2. and 4 with t<=1.5 in. in perimeter

columns

60.817 82,558 1.115 0.903

14 All 60 ksi Plates 1, 2. and 4 w ith t<=1.25 in. in perimeter

columns

62.027 87,250 1 .1 78 0.894

15 All 65 ksi Plates 1, 2. and 4 with t<=0.5 in. in perimeter columns^

69,642 90,442 1.221 0.979

16 All 70 ksi Plates 1 . 2. and 4 in. perimeter columns 76.735 91,951 1.242 0.955 r All 75 ksi Plates 1, 2. and 4 in perimeter columns 82.469 96.821 1.308 0.936

1AU 80 ksi penmeter columns steels, regardless of plate 91.517 99.442 1 .343 0.987

19 All (83. 90. 100) ksi penmeter column steels, regardless of plate104,783 1 15,983 1 .566 0.976

20 Laclede truss web bar rounds specified as A36 38.067 59,567 1.004 0.935

21 Laclede truss chord angels (regardless of ASTM Spec) and all rounds specified as A242

55,332 74.050 1.000 0.959

22 A325 bolts' 104.783 115,983 1.566 0.976

23 All 42 ksi Plate 3 in perimeter columns 42.600 67.216 0.900 0.912

24 .Ml 45 ksi Plate 3 in perimeter columns 45,900 69,831 0.940 0.921

25 All 50 ksi Plate 3 in perimeter columns 51,400 74,188 1.000 0.935

26 A\] 55 ksi Plate 3 in perimeter columns 56,900 78,546 1.070 0.906

-17 .Ml 60 ksi Plate 3 in perimeter columns 62,400 83,903 1.130 0.949

28 All 65 ksi Plate 3 in perimeter columns 67,900 87,261 1.190 0.975

29 All 70 ksi and 75 ksi Plate 3 in perimeter columns 78,900 95,976 1.310 0.997

a. Steels in the following members are assumed to have the propenies shown in the table: 36 ksi plates and straps (Material 1 ). 36 ksi channels, tubes, and "rigid" beams (Material 2). 50 ksi channels and plates (Material 12).

b. 65 ksi steels in perimeter columns with t>0.5 in. are assumed to have the same properties as those in Material 1 5.

c. In the column model, stress-strain relationships of bolts are used. Note: Bolt properties are assumed to be the same as those in Material 19.

NISTNCSTAR 1-6C, WTC Investigation 15
Chapter 3

Table 3-2. Parameters for K(T) and n(T).

a,7fr = 36,000 psi OyRT> 36,000 psi

tkl, T 524.1812 511.8266

tk2, °C 523.6799 511.8938

kO, psi 29049.2 26472.1

kl 9.4346 6.5764

k2 9.3532 6.5971

k4, psi 121605.6 122516.7

tnl, T 524.4304 519.634

tn2, °C 521.241 499.6031

nO, psi 0.1235 0.0342

nl 19.0000 10.0000

n2 19.0000 V 10.0000

n4. psi 0.2168 0.1511

Figure 3^ shows stress-strain curves of Material ID 1 (see Table 3-1 for the material description) at room and elevated temperatures. Figure 3-4 (a) is a close-up view of the lower strain range, while

Fig. 3-4 (b) shows strain levels up to 0.3. The elastic-plastic behavior of steels was modeled with ANSYS material model "Multi-linear isotropic

hardening von Mises plasticity."

0 0.UU5 0.01 0.015 0,02 0,025 0.03

Elastic + Plastic Strain (in/in) — T=RT

T=300°C T=500°C

T=700°C

(a) Strain < 0.03 (b) Strain < 0.3

Figure 3-4. Steel (Material ID 1) stress-strain relationships at different temperatures.

16 NISTNCSTAR 1-6C, WTC Investigation
Materials

Creep: Steel creeps at elevated temperatures (T > 350 °C). The creep behavior of the steels in the WTC

towers was expressed by NIST as follows:

V60y

70.5-

cr \c(T)

(7iiRT J

(7)

where:

0

|Q-(6.1+0.00573r)

I Q-( 1 3.25-0.0085 ID

for r<350'C

for 350X<r<500°C

for 500°C<r< 725 C

6(7) = -1.1 + 0.00357 for T<125'C

c(r) = 2.1 + 0.00647 for T <liy C

(7-a)

(7-b)

(7-c)

The creep model was validated against experimental data by NIST (NIST NCSTAR 1-3D). The creep

model was derived by modifying the creep model already developed by Fields and Fields (1991). In this original model, the stress was scaled by yield strength at room temperature. The original model was used

in the truss model and the exterior wall model.

The function. a{T) . is not smooth at 7= 500 °C. To enhance numerical efficiency, a{T) was modified

by smoothing it as follows:

a(7) =

10

10

-(13.25-0.00851x20)

M 13.25-0.008517")

for 7 < 20° C

for 20X<7< 725°C

(7-d)

A comparison of creep strains calculated from Eq. (7) with a{T) given by Eqs. (7-a) and (7-d) is shown

in Fig. 3-5. For 350 °C < 7 < 500 °C, creep strain is underestimated with a{T) by Eq. (7-d).

However, the difference is small, and creep strains for temperatures below 500 °C are usually negligible.

Figure 3-6 illustrates creep behavior of steel at elevated temperatures for Material ID 1 . Figure 3-6 (a)

shows creep strain rate at different stress levels and different temperatures, and Fig. 3-6 (b) compares

elastic, plastic, creep, elastic plus plastic, and total strains at 7= 600 °C and after loading at a constant

stress level for 1,800 s. The creep model expressed by Eq. (7) with a{T) given by Eq. (7-d) was used in the global models.

In ANSYS analysis, the "time hardening" implicit creep model was used for BEAM 188 and BEAM189

elements, where creep strain rate was given by:

^= CAT)a'^-'''t'^''' (8)

dt

'

and C| (7) , C^iT) , and C3 (7) are temperamre-dependent parameters derived from the creep model

expressed by Eq. (7) with the following relationships:

NIST NCSTAR 1-6C, WTC Investigation 17
Chapter 3

' 100

C,{T)^c{T)

C,{T) = b{T)-\

r 1 \*<^>

V60y

^70.5^

c(T)

For BEAM24 elements in ANSYS, the primary explicit creep model was used. Creep strain rate was

specified by

dt = M{T)K{T)a""'t N{T).M(T)-\

(9)

where

M{T) = b{T)

N{T) = c(T)

K{T) = -^a{T)

100

r 1 ^'"^>

V60y

70.5

V ^kRT J

The truss model and the exterior wall subsystem model included creep with BEAM 188 and 189 elements.

The global model included creep with BEAM24 elements, as they were more numerically stable for creep

and post-buckling behaviors.

300 350 400 450 500 550 600 Temperature (°C) —— Original a(T)

••••• Modified a(T)

Figure 3-5. Comparison of creep strains with a{T) given by (7-a) and (7-d) for

Material ID 1 steel subject to 15 ksi for 1,800 s at a given temperature.

18 NISTNCSTAR 1-6C, WTC Investigation
Materials

110

1 10

T=400°C T=550°C

T=700°C

2 10 3 10 4 10 Creep Strain Rate (in/in/sec)

Elastic

Plastic Creep

Elastic + Plastic Total

(a) Creep strain rate (b) Comparison of different strains at T= 600 'C and t= 1,800 s

Figure 3-6. Creep behavior at elevated temperatures for Material ID 1 steel.

3.2.3 Steel Failure Criteria

The tensile failure criteria for steel were defined in terms of plastic strains. The multi-axial fracture strain criterion for different steels and temperatures in terms of true stress and true strain (NIST NCSTAR 1-3D)

can be expressed as follows:

£r - a{T)exp

2 G

(10)

cir(r) is a temperature dependent material property, values of which can be calculated from Table 3-3 by

using Eq. (11). For the uniaxial stress condition, where g — g and cr,„ = (j/3 , the plastic strain at fracture reduces to:

^/ ,„„ =a(nexp(-0.5) (11)

Table 3-3 shows the uniaxial plastic strain at fracture, 8^ , calculated by Eq. (11 ) for different

temperatures. This criterion is valid for a finite element analysis (PEA) with a very fine mesh. For a coarser mesh, the equivalent steel fracture criterion was determined numerically as follows. A standard

tension test specimen was modeled in ANSYS. The gauge length, width, and thickness of the specimen were 8 in, 1.5 in, and 1 in., respectively, and steel properties of Material ID 1 were used. Six different

models (Model 0 to 5) were created, each having a different mesh size. Element sizes of Models 0 to 5 were 0.025 in., 0.050 in., 0.0125 in., 0.250 in., 0.375 in., and 0.75 in. It was assumed that Model 0 was a

fine mesh that was able to capture tensile fracture in uniaxial tension.

Model 0 was subjected to tension until the maximum plastic strain in the direction of applied

displacement reached the uniaxial fracture strain determined by Eq. ( 1

1 ) for uniaxial stress condition, and

the corresponding elongation of the specimen, Ao, was obtained. Models 1 to 5 were then subjected to the same elongation, Ao, and the maximum plastic strain in the direction of applied displacement was

measured for each model. The maximum plastic strain due to the elongation of Ao was defined as the

limiting plastic strain (equivalent fracture plastic strain) for the corresponding element size.

NIST NCSTAR 1-6C, WTC Investigation 19
Chapter 3

From these six cases, a relationship between element size and equivalent uniaxial fracture plastic strain was established. This process was repeated for temperatures 20 °C, 100 °C, 300 °C, 500 °C, and 700 °C.

Figure 3-7 (a) shows the ratio of the maximum plastic strain in the direction of applied displacement due

to displacement Ao to uniaxial plastic strain by Eq. (1 1) vs. element size at different temperatures. The

FEA results were extrapolated up to the element size of 50 in. Plastic strain shown in Fig. 3-7 (b) was

used as the failure criterion for the corresponding element size in the FEA. Note that Fig. 3-7 (b) shows

the failure criterion for element size larger than 0.375 in.

The compressive failure criteria for steel were not specified explicitly in tenns of plastic strains because

the information was not available. However, failure of compressive members was expressed by elastic buckling and plastic kink-type buckling (see Chapter 6) of compression members.

Table 3-3. Uniaxial plastic strain at fracture by Eq. (11).

Material ID

Plastic Strain at Fracture in the Uniaxial Test, £ / iini

20 °C 100 °c 300 °C 500 °C 700 X 1000 °c

1 0.8411 0.6989 0.6610 1 .0446 1.8100 3.5862

2 0.8411 0.6989 0.6610 1 .0446 1.8100 3.5862

3 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

4 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

5 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

7 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

8 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

9 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

10 0.8891 0.7388 0.6987 1.1042 1.9142 3.7907

11 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

12 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

13 0.2846 0.2364 0.2236 0.3534 0.6123 1.2132

14 0.3774 0.3136 0.2965 0.4686 0.8120 1.6088

15 0.5338 0.4436 0.4195 0.6629 1.1486 2.2758

16 0.5623 0.4672 0.4418 0.6983 1.2099 2.3972

17 0.7752 0.6442 0.6092 0.9628 1.6681 3.3051

18 0.6545 0.5439 0.5143 0.8129 1.4084 2.7906

19 0.4254 0.3535 0.3343 0.5283 0.9154 1.8137

20 0.8411 0.6989 0.6610 1.0446 1.8100 3.5862

21 0.4908 0.4078 0.3857 0.6095 1.0561 2.0924

20 NISTNCSTAR 1-6C, WTC Investigation
Materials

0.01 0.10 1.00 10.00 100.00 0 100 200 300 400 500 600 700 Element Size (in) Temperature (°C)

(a) FEA results and extrapolation (b) Recorrmnendeci limiting plastic strain

Figure 3-7. Maximum plastic strain from the finite element analysis

and limiting plastic strain.

3.3 WELDS

The weld properties at all temperatures were assumed to be the same as those of the base metal of the same ultimate tensile strength as determined by Project 3. High temperature properties of the weld metals were not found in the literature. Susceptibility of existing cracks in the welds to growth (fracture

toughness) does not increase with temperature (Stevick 1994). This assumption was supported by the

following observations in the recovered WTC steel: the exterior column welds were strong enough to fail the base metal, the obser\'ed fractures in the exterior columns were mostly through the base metal, and the

welds in trusses were resistance welds with no filler added. For the core columns, the area of the welds was significantly less than that of the base metal, and several fractures through the welds were observed.

Fractures in the truss seats and truss connections were also observed.

3.4 BOLTS

A load-elongation relationship for a 7/8 in. A325 bolt with 4 in. length at room temperature was provided

by Project 3. Load-elongation relationships at elevated temperatures are constructed by scaling the loads

by the yield and ultimate tensile strength reduction factors for bolt steels shown in Fig. 3-3 (c) and (d). Figure 3-8 shows the load-elongation relationships of a 7/8 in. bolt at different temperatures. Loadelongation relationships of A32 5 bolts of different size were created by proportioning the load by the net

area.

The load-elongation relationship for bolts with a different length than 4.0 in. is expected to be very

similar to the load-elongation relationship for 4.0 in. length since bolt deformations are localized.

Based on the AISC formulas (AISC 2003), C-J3-2 to C-J3^, the shear strength for a single shear plane is calculated as 0.67 of the tensile strength given in Fig. 3-8 when threads are excluded from the shear

plane. When threads are not excluded from the shear plane, the nominal shear strength for a single shear

plane is 0.53 of the tensile strength given in Fig. 3-8. These factors were obtained by a ratio between the

shear strength and the tensile strength evaluated by the AISC formulas. No shear ductility was assumed

at failure.

NISTNCSTAR 1-6C. WTC Investigation 21
Chapter 3

80,000 n

70,000 - - -

0.000 0.050 0.100 0.150 0.200 0.250 Elongation (in.)

Figure 3-8. 7/8 in. A325 bolt load-elongation curves at elevated temperatures.

3.5 COEFFICIENT OF FRICTION

The coefficient of friction of 0.33 for calculation of shear in friction-type connections was used. This

value was taken from the AISC LRPD (2003) friction coefficient for uncoated clean mill scale steel surfaces, or surfaces with Class A coatings on blast-cleaned steel surfaces.

3.6 SYMBOLS

a{T) = temperature-dependent material property that defines fracture criterion

a,XT) = instantaneous coefficient of thermal expansion of concrete ^s(n = instantaneous coefficient of thennal expansion of steel = steel yield strength reduction factor due to elevated temperature

PAT) = steel ultimate strength reduction factor due to elevated temperature

Yc unit weight of concrete (110 pcf and 1 50 pcf for lightweight and normal weigh

respectively)

Ys unit weight of steel (490 pcf = 0.284 pci for all steel types at any temperature)

concrete strain at maximum compressive stress

creep strain of steel

elastic strain

elastic plus plastic strain = effective plastic strain at fracture

^f _ uni uniaxial plastic strain at fracture

plastic strain

concrete strain at maximum tensile stress

concrete strain at full crack formation (separation) in tension

22 NISTNCSTAR 1-6C, WTC Investigation
Materials

— Poisson's ratio of concrete = Poisson's ratio of steel a = effective von Mises stress

(T„ = mean stress

(T^i^j = room temperature yield strength of steel

(T^i^j- - room temperature tensile Strength of steel

(T) = modulus of elasticity of steel

(T) = modulus of elasticity of concrete = mix design factor = ratio of the actual 28 day cylinder strength to f' = in-situ factor = ratio of in-situ 28 day strength to the 28 day cylinder strength

F3 = aging factor = ratio of mature concrete strength to 28 day concrete strength — actual strength of in-place concrete

fl - specified 28 day strength

f^{T) = compressive strength of concrete

f,{T) = tensile strength of concrete K(T) - sigmoidal function of temperature with six parameters

niT) = sigmoidal function of temperature with six parameters — correction factor that has the following two functions: ( 1) to correct the strain rate effect introduced in the material testing and create the stress-strain curve for zero strain rate, and (2) to match the room temperature stress-strain curve at strain of 0.05

Rj^^ = ratio of the room temperature tensile strength of the steel of interest to the room

temperature tensile strength of the steel used to develop the power law model

RT = room temperature (20 °C)

NISTNCSTAR 1-6C, WTC Investigation 23
Chapter 3

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24 NISTNCSTAR 1-6C, WTC Investigation
Chapter 4

Model Conversion From SAP to ANSYS

Reference structural models were developed under Project 2 in SAP2000 (SAP) for traceability to a verified data set (NIST NCSTAR 1-2, NIST NCSTAR 1-2A). The SAP2000 Floor 96 model of WTC 1 and the SAP global models of WTC 1 and WTC 2 were converted into ANSYS 8.1 (ANSYS) and used as

a foundation for developing detailed structural models. The converted ANSYS models were modified to incorporate the nonlinear behaviors of the components for the thermal/structural evaluation of collapse

initiation.

4.1 TRANSLATION PROCEDURE

An automatic translation software was developed to partially convert the floor model and global models

from SAP to ANSYS:

• The Joints, Frames, and Shells in the SAP model were translated into ANSYS Keypoints,

Lines, and Areas. Translation using geometry definition, instead of nodes and elements,

allowed for easy mesh refinement, where needed.

• Lines were meshed with both section properties and real constants so that a translation

between 3-D elastic beam (BEAM44) elements and 3-D inelastic finite strain beam

(BEAM 188/BEAM 189) elements was achieved by simply changing element types. Areas were meshed with elastic shell (SHELL63) elements in ANSYS to match the Shell elements

in SAP. Lines and Areas were able to be changed to nonlinear beam (BEAM 188) and

nonlinear shell (SHELL181) elements simply by changing an element type.

• Material properties were assigned as described in Chapter 3 based on the material definitions

and Frame section properties in SAP.

• Frame section properties in SAP were converted into Real Constants for BEAM44 in ANSYS. Cross section properties in SAP were retained for fumre conversion into cross section data for BEAM 188 elements. Shell thicknesses in SAP were converted into Real

Constants for SHELL63 in ANSYS.

• Joint restraints in SAP were translated into DOF constraints in ANSYS.

• Frame distributed loads and area uniform loads were translated into surface loads on Lines

and Areas in ANSYS.

• The ANSYS BEAM44 elements support element moment releases, but the ANSYS nonlinear

BEAM188 elements do not. Therefore, Frame releases in SAP were modeled by coincident

nodes with coupled (CP) degrees of freedom in ANSYS.

• The ANSYS BEAM44 elements allow beam end offsets in three directions, but the ANSYS

nonlinear BEAM 1 88 elements only allow beam end offsets perpendicular to the element axis

through section offset (SECOFFSET) command. Frame insertion points in SAP were

converted in two ways. For offsets along the element axis, additional nodes and rigid

MPC184 elements with the proper lengths were used in ANSYS. For offsets perpendicular to

NIST NCSTAR 1-6C, WTC Investigation 25
Chapter 4

the element axis, beam end offsets were defined using Real Constants for BEAM44, and were

defined using SECOFFSET command for BEAM 188.

• Frame offsets and rigid panel factor in SAP were modeled by adding additional nodes and

rigid beam MFC 1 84 elements with the proper lengths in ANSYS.

During the conversion of the SAP floor model, the following conditions were encountered and were

resolved:

• The SAP floor model allowed automatic division of the frames at joints. This caused

problems in the translation software, because the frame connectivities in the Graphical User

Interface did not show the actual internal element connectivities used in the SAP analysis

engine. In order to resolve this problem, the translation software was modified to use the

internal element connectivities. The table of internal connectivities was exported from the

SAP model after the execution of the SAP analysis.

• Infonnation on automatic offsets in the SAP model were not available in the SAP input file. The table of element offsets was exported after the execution of the SAP analysis.

• There were both intentional and unintentional duplicate elements in the SAP floor model that led to problems in the translator since ANSYS cannot have duplicate lines sharing the same

keypoints. Some duplicate elements were used to model additional steel plates at the ends of

trusses. The duplicate elements were manually deleted, and the section properties of the

remaining elements were modified to account for the additional steel. Some duplicate

elements were from frame elements with different lengths that overlapped. These were

manually corrected.

Those parts of the model that were not converted by the translation software were converted manually.

Table 4-1 presents the descriptions of finite elements used in ANSYS models, such as BEAM188

(ANSYS, Inc. 2004). All structural elements listed in the table including link, beam, shell, and solid

elements can be used with temperature-dependent material properties.

26 NISTNCSTAR 1-6C, WTC Investigation
Model Conversion From SAP to ANSYS

Table 4-1. Element types used in ANSYS models.

Name Element Type Description

LINKS 3-D truss LINK8 is a uniaxial tension-compression element with three degrees of fi^eedom

at each node. It has plasticity, creep, and large deflection capabilities.

BEAM4 3-D elastic beamBEAM4 is a 3-D elastic Euler beam element. The element has six degrees of

freedom at each node. Large deflection capabihty is included. 3-D elastic tapered

unsymmetric

beam

BEAM44 is a 3-D elastic Euler beam element and allows a different unsymmetrical geometry at each end. The element has six degrees of freedom

at each node. Large deflection capability is included.

BEAM 188 3-D linear

finite strain beam

BEAM 188 is a linear (2-node) or a quadratic beam element in 3-D based on Timoshenko beam theory. Each node has six degrees of freedom or seven

degrees of freedom (6+warping). Shear deformation effects are included. This

element is supported for plasticity, creep, large deflection. A cross section can be a built-up section referencing more than one material. Creep strain is calculated by implicit time integration method.

BEAM 189 3-D quadratic

finite strain beam

BEAM 189 is a quadratic (3-node) beam element in 3-D based on Timoshenko

beam theor>'. Each node has six degrees of freedom or seven degrees of

freedom (6+warping). This element is supported for plasticity, creep, large

deflection. A cross section can be a built-up section referencing more than one

material. Creep strain is calculated by implicit time integration method.

SHELL63 4-node elastic shell SHELL63 has both bending and membrane capabilities. The element has six degrees of fi-eedom at each node: three translations and three rotations. Large

deflection capability is also included. SHELLI81 4-node finite strain shell SHELL181 is a 4-node shell element with six degrees of freedom at each node:

three translations and three rotations. Plasticity, creep, and large deflection

capabilities are supported. In nonlinear analyses, change in shell thickness is accounted for. SHELL181 may be used for layered applications.

SOLID 185 3-D 8-node

structural solid SOLID 185 is an 8-node structural solid element and has three degrees offreedom at each node (three translations). Plasticity, creep, and large deflection

capabilities are supported.

COMBIN37 Control

element

COMB1N37 is a unidirectional element with the capability of turning on and off during an analysis. The element has one degree of freedom at each node. MFC 184 Multipoint

constraint element

MPC184 comprises a general class of muhi constraint elements that implement

kinematic constraints using Lagrange multipliers. Depending on the option that the user selects, the element can be used as a rigid link element, a rigid beam

element, a slider element, a spherical element, a revolute joint element, and a universal joint element.

NIST NCSTAR 1-6C, WTC Investigation 27
Chapter 4

4.2 VALIDATION

4.2.1 Floor Model Validation

Figures 4-1 through 4^ show the converted floor model.

The following analyses were performed to validate the converted ANSYS floor model against the original

SAP model.

• One static analysis with gravity loads, defined in SAP as Load Case "DEAD," included self- weight plus 3.5 psf unifonn load in the office area.

• One modal analysis, using structural mass only.

Table 4-2 summarizes the comparison of the SAP and ANSYS results for the gravity load case. The total reactions for the SAP and ANSYS models were within 0.1 percent of each other. The maximum slab

displacement predicted by the ANSYS model was 3.2 percent smaller than that obtained from the SAP

model. The defonned shapes of the gravity load case for the SAP and ANSYS models are shown in Figs. 4-5 and 4-6.

Table 4-2. Comparison of SAP and ANSYS results for gravity load case. SAP ANSYS

Total reaction, kip 2,212.81 2,210.85 (-0.09 %)

Maximum slab displacement, in. 0.718 0.695 (-3.2 %)

Figure 4-1. Converted ANSYS model for Floor 96 of WTC 1: overall view.

28 NISTNCSTAR 1-6C, WTC Investigation
Model Conversion From SAP to ANSYS

Figure 4-2. Converted ANSYS model for Floor 96 of WTC 1 : partial view

near corner of building.

NISTNCSTAR 1-6C, WTC Investigation 29
Chapter 4

AN

ELEMENTS

JUN 2 2004

Figure 4-4. Converted ANSYS model for Floor 96 of WTC 1 : view of

floor beams and columns.

Figure 4-5. Deformed shape (x100) of gravity load case for SAP floor model (downward

displacement is negative).

30 NISTNCSTAR 1-6C, WTC Investigation
Model Conversion From SAP to ANSYS

Figure 4-6. Deformed shape (x100) of gravity load case for

ANSYS floor model (total displacements are shown).

Table 4-3 summarizes the comparison of the SAP and ANSYS resuUs for the modal analysis of the floor

models. The total masses of the SAP and ANSYS models were within 0.02 percent of each other. The

dominant natural frequency of the floor predicted by the ANSYS model was 2.5 percent higher than that obtained from the SAP model. This discrepancy is consistent with the discrepancy observed for gravity

displacement. The dominant mode shapes of the floor for SAP and ANSYS models are shown in Figs. 4-7 and 4-8.

Table 4-3. Comparison of SAP and ANSYS floor model modal analysis results. SAP ANSYS

Total mass. Ib sec" in. 5448.7 5447.7 (-0.02 %)

Dominant natural frequency of floor. Hz 4.32 4.43 (+2.5 %)

NISTNCSTAR 1-6C. WTC Investigation 31
;t2- -aae, a84 070 use n&^Asx au 0

gure 4-7. Dominant mode shape (frequency = 4.32 Hz) of floor structure

for SAP floor model.

gure 4-8. Dominant mode shape (frequency = 4.43 Hz) of floor structure

for ANSYS floor model.

NISTNCSTAR 1-6C, WTC Investigation
Model Conversion From SAP to ANSYS

4.2.2 Global Model Validation

The translated ANSYS models were subjected to gravity dead and live loads and the results were compared to the results of SAP2000 global models (Figures 4-9 and 4-10). This comparison was

performed to verify the accuracy of the translation of the SAP2000 models into ANSYS. The overall

displaced shapes, the maximum displacements and vertical base reactions at each construction stage, and

element forces for a set of randomly selected members from different parts of the buildings were

compared.

The gravity' analysis consisted of three stages that simulated the construction sequence of the buildings.

Stage 1 was the analysis of the parts of the towers up to and including Floor 106 under their self weight.

In Stage 2, the members above Floor 106 in unstressed states were added to the parts of the towers up to and including Floor 106. which had already deformed under their self-weight, and the towers were

subjected to and analyzed for the dead load of the newly added members. In Stage 3, the towers were

subjected to and analyzed for the additional load consisting of the superimposed dead load and 25 percent

of the design li\ e loads were added to the existing dead loads.

Figures 4-1 1 and 4-12 compare the deformed shapes of WTC 1 and WTC 2 obtained from the translated

ANSYS models to the ones obtained from the SAP models at the end of Stage 3 of the gravity analysis.

Table 4—4 and Table 4-5 summarize the maximum displacement and vertical reactions at the base for all stages of the gravity analysis. As can be seen, the deformed shapes and the maximum displacements and

vertical reactions obtained from the analyses performed with the translated ANSYS models agree well

with the results of the SAP analyses. The maximum differences between the two models were less than

1.4 percent for WTC 1 and 0.7 percent for WTC 2 for the displacements, and 1.2 percent for WTC 1 and

0.3 percent for WTC 2 for the base reactions.

Table 4-6 and Table 4-7 show the comparisons of the axial forces computed from ANSYS and SAP2000

for a randomly selected set of elements from different parts of each building. In Table 4-6 and Table 4-

7, the axial force values that are less then 0.5 kip are shown as 0.0 kip. There is good agreement between

the results obtained from ANSYS and SAP models.

NISTNCSTAR 1-6C. WTC Investigation 33
Chapter 4

Figure 4-9. Converted ANSYS model of WTC 1.

Figure 4-10. Converted ANSYS model of WTC 2.

34 NISTNCSTAR 1-6C, WTC Investigation
Model Conversion From SAP to ANSYS

z

X

X

y

Maximum displacement = 5.07 in

(a) WTC 1 ANSYS Model at Stage 3 (b) WTC 1 SAP2000 Model at Stage 3

(Displacement contour is only shown on floor

(shell) elements.)

Figure 4-1 1 . Displaced shape of WTC 1 at the end of gravity analysis.

(a) WTC 2 ANSYS Model at Stage 3

z

X y

Maximum displacement = 8.14 In .

(b) WTC 2 SAP2000 Model at Stage 3

(Displacement contour is only shown on floor

(shell) elements.)

Figure 4-12. Displaced shape of WTC 2 at the end of gravity analysis.

NISTNCSTAR 1-6C, WTC Investigation 35
Chapter 4

Table 4-4. Comparison of maximum displacements and base reactions of WTC 1 from

translated ANSYS and SAP2000 models.

Stage

Maximum Vertical Displacement (in.) Base Reaction Sum (kip)

ANSYS SAP2000

Percent

Difference ANSYS SAP2000

Percent

Difference

1 -2.87 -2.83 1.4 55.600 54,940 1.2

2 -4.76 -4.74 0.4 98,470 97,850 0.6

3 -5.09 -5.07 0.4 107.040 106,450 0.6

Table 4-5. Comparison of maximum displacements and base reactions of WTC 2

obtained from translated ANSYS and SAP2000 models.

Stage

Maximum Vertical Displacement (in.) Base Reaction Sum (kip)

ANSYS SAP2000

Percent

Difference ANSYS SAP2000

Percent

Difference

1 -5.87 -5.91 -0.7 125,050 124,680 0.3

2 -7.67 -7.71 -0.5 166.950 166,980 0.0

3 -8.10 -8.14 -0.5 180.250 180,360 -0.1

Table 4-6. Comparison of axial forces in randomly selected elements from WTC 1 model

Location and Type of Selected Element

Axial Force (kip)

ANSYS SAP2000

Exterior Column 302 at Floor 104 -77 -69

Spandrel between Columns 124 and 125 at Floor 102 0 0

Outrigger member between at Floor 1 10 -39 -48

Vertical hat-truss member at 1005 core column line at Floor 109 -74 -91 Horizontal hat-truss member at Floor 107 21 19

Horizontal hat-truss member at Floor 108 170 150

Core Column 602 at Floor 97 -738 -745

Core Column 501 at Floor 93 -2.180 -2,190

Core Column 1001 at Floor 89 -2.570 -2,590

Spandrel between Columns 339 and 340 at Floor 100 0' 0

Axial force values less than 0.5 kip are shown as 0.0 kip.

36 NISTNCSTAR 1-6C, WTC Investigation
Model Conversion From SAP to ANSYS

Table 4-7. Comparison of axial forces in randomly selected elements from WTC 2 model

at the end of gravity analysis.

Location and Type of Selected Element

Axial Force (kip)

A1>J>YS »ArzUUU

f~"nrp hpam at Plnnr 1 07 11 6

TnrlinpH tnt*is mpmhpr at Hfit-trii<sQ at Plnnr 107 -34 -4

lllV^llilvU TnplinpH tni^^ Ll tl^^ mpmHpr IJl^lliU^l cll at Hat-tniQQ liul 11 LlDo atU.I 1Flnnr IwLli lOR l\JO 36 8

i_lldllitl-l TnrlinpH triw*; 11 Ll^^ lll^lllLfd mpmhpr cll at liat-trii*;*; liCll 11 LlOO atdL XPlnnr lUUl 108 XV/O -580 -670

r^nrp V_ VJl t r^oliimn \_ VJl Lllllll w'V/— SO'' atClL 1Plnnr lwv/1 R7O / -1,930 1,940

Cnre V. Ul t rnliimn \^UlU.illll 11001 V/W 1 atill 1Flnnr 1\JV_»1 R? -3.270 -3.290 Tore V_ Wl t rnliimn V_ v/1 Llillll 1Iv/W*- 00'> attil XFlnnr i\J\Jl 87xj 1 1 n 1 A

-i.yio -1,920

Core Column 1 008 at Floor 82 -3,400 3.520

Core Column 1003 at Floor 107 -590 -608

Exterior Column 122 at Floor 82 -313 -313

Exterior Column 329 at Floor 82 -228 -230

Exterior Column 130 at Floor 107 -222 -202

Spandrel between Columns 138 and 139 at Floor 83 0* 0

Spandrel betw een Columns 447 and 448 at Floor 87 0 0

* Axial force values less than 0.5 kip are shown as 0.0 kip.

4.3 SUMMARY

In general, the results from the translated ANSYS floor and global models showed good agreement with

the results obtained form the SAP models. For the floor model, the calculated base reactions and

displacements due to gravity load showed a 3 percent difference between the ANSYS and SAP models.

Similarly, the modal analysis results showed a 3 percent difference in calculated total mass and the

fundamental frequency between the ANSYS and SAP floor models.

For the global models, the comparison of base reactions and the maximum displacements in the vertical

direction showed that the maximum differences between the ANSYS and the SAP models were less than

1 .4 percent for WTC 1 and 0.7 percent for WTC 2 for displacements, and 1.2 percent for WTC 1 and

0.3 percent for WTC 2 for base reactions. Comparison of axial forces for both global models showed

good agreement between ANSYS and SAP models.

Based on these comparisons it was concluded that the translation of the floor and global models from

SAP to ANSYS was acceptable, and the translated models were used to investigate the component and

building responses under the presence of non-linear material properties and thermal effects.

NISTNCSTAR 1-6C, WTC Investigation 37
Chapter 4

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38 NISTNCSTAR 1-6C, WTC Investigation
Chapter 5

Full Floor Subsystem

5.1 OBJECTIVE

The failure modes and the corresponding failure loads of key components of the full floor subsystem were

identified and were evaluated at elevated temperatures through analysis of detailed models of these

components, using either hand calculations or finite element analysis. Key floor components analyzed

included truss seats, knuckle (truss-to-slab shear connector), and a 3-D model of a single truss and a corresponding section of concrete slab. Finite element models that can capture the failure modes with

efficiency and determine the failure loads were then developed. These models of key components were

incorporated in the full floor subsystem model.

Likely failure modes of truss seats were identified, and the corresponding failure loads were determined

and are reported in this section. The following loading conditions were considered: vertical force,

horizontal tensile force, horizontal compressive force, and combined vertical and horizontal force.

The floor truss was supported at the exterior wall and at the core by truss seats. The truss seats at the

exterior wall and at the core are referred to as exterior truss seat and interior truss seat, respectively.

The interior truss seat consisted of a horizontal plate with two vertical plate stiffeners as shown in Fig. 5-1 . These plates were fillet welded together and fillet welded to the core channel beam. Two

5/8 in. diameter A325 bolts (one bolt in each truss) connected the truss to the seat. The bolted connection was a friction type with 3/4 in. x 1 3/4 in. (width x length) long slotted holes in the seat horizontal plate

and 7/8 in. oversize holes in the bearing angles.

The exterior truss seat consisted of a seat angle attached to the spandrel with two vertical plates (stand-off

plates), and a gusset plate as shown in Fig. 5-2. Fillet welds connected the seat angle to the stand-off

plates, the stand-off plates to the column/spandrel, and the gusset plate to truss top chord. A completejoint-penetration groove weld connected the gusset plate to the column/spandrel. Similar to the interior truss seat, each pair of trusses was attached to the exterior truss seat by two 5/8 in. A325 bolts. The

bolted connection was a friction type with 3/4 in. x 2 in. long slotted holes in the seat angle and 7/8 in. oversize holes in the truss bearing angle.

In Floor 96 of WTC 1, there were seven types of interior truss seats and eight types of exterior truss seats. The different types of interior truss seats were identified with Detail Numbers 15, 1 7, 20, 21, 22, 23, and

226A;and the exterior truss seats with Detail Numbers 1013, 1111, 1212, 1311, 1313, 1411, 1511, and

161 1, as shown in Fig. 5-3.

All interior truss seat types were similar in their design geometry, but with different sizes of vertical and

horizontal plates, locations of the bolt holes, and sizes of the fillet welds. The thicknesses of plates

ranged from 3/8 in. to 3/4 in.; the distance between bolt holes ranged from 8 1/2 in. to 10 1/2 in.; and the

size of the fillet welds ranged from 1/4 in. to 3/8 in. All exterior truss seat types were also similar in their

5.2 TRUSS SEATS

5.2.1 Description of Truss Seats

NISTNCSTAR 1-6C, WTC Investigation 39
Chapter 5

design geometry, but with different sizes of stand-off plates, sizes of seat angles, sizes and shapes of

gusset plates, locations of bolt holes, and sizes of fillet welds. The vertical heights of the stand-off plate

ranged from 8 in. to 1 1 in. The seat angle sizes ranged from L4 x 4 x 1/2 to L6 x 4 x 3/4. The gusset

plates were rectangular and trapezoidal and ranged in width from 4 1/2 in. to 6 in. The distance between

boh holes ranged from 3 1/4 in. to 10 1/2 in.; where it was 3 1/4 in., the seat was supporting a single truss

in lieu of a pair of trusses. The size of the fillet welds ranged from 5/16 in. to 3/8 in.

Side View Front View Top View

Figure 5-1. Interior truss seat.

Side View Front View Top View

Figure 5-2. Exterior truss seat.

40 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Reproduced with permission of The Port Authoritv of New York and New Jersey.

Figure 5-3. Truss seat detail location on northeast quadrant of Floor 96 of WTC 1.

5.2.2 Truss Seat Material Properties

The material properties used in the calculations were selected from Table 3-1 to best match the material

properties indicated on the design drawings. Figure 3-3 was used to determine the mechanical properties

at high temperature. The materials used for truss seat calculations are shown in Table 5-1

NISTNCSTAR 1-6C. WTC Investigation 41
Chapter 5

Table 5-1. Materials used for truss seat calculations.

Description

Selected Material

ID

Exterior and interior truss seat A325 bolts Material 22

Fillet welds Material 7

Truss bearing angles Material 21

Exterior truss seat Seat angle Material 1 Gusset plate Material 12

Stand-off Material 23

Truss top chord angles Material 21

Cover plate for bridging truss top chord Material 1

Interior truss seat Vertical plate stiffener Material 12

Horizontal plate Material 12

5.2.3 Truss Seat Failure Modes and Sequence

Possible failure modes for truss seats were identified for vertical force, horizontal tensile force, horizontal

compressive force, and combined vertical and horizontal force. For each failure mode, the truss seat capacity was detennined at different temperatures.

Failure Modes ofExterior Truss Seats for Vertical Force: The vertical load on the seat was eccentric to the plane of connection between the seat and the spandrel. Because of this eccentricity, the trtiss seat resisted to combined effect of both shear and bending. Finite element analysis of the truss seat was

performed to determine load paths and evaluate the behavior of the seat connection.

Figure 5-4 shows the finite element model of the exterior truss seat connection. Half of the truss seat was

modeled and symmetry boundary conditions were applied to all nodes in the plane of symmetry. The

results of the finite element analysis showed that shear force was carried primarily by the stand-off plates,

while the bending moment was resisted by tensile force in the gusset plate and compressive force in the

stand-off plate. The seat angle restrained the moment until horizontal force in the connection caused

slippage between the seat angle and bearing angle. The truss seat capacity was governed by the capacities

of fillet welds at the stand-off plate to spandrel connection subjected to shear, bending, and compression.

The failure mode was the fracture of the fillet welds between the stand-off plates and spandrel, resulting

in loss of vertical support.

Failure Modes ofInterior Truss Seats for Vertical Force: The vertical load on the truss seat was

eccentric to the plane of fillet weld connection between the truss seat vertical plate stiffeners and the

channel beam. Calculations showed that the truss seat capacity was governed by the capacities of the

fillet welds at this joint subjected to shear and bending. The failure mode was the fracture of the fillet welds between the vertical plate stiffeners and the channel beam, resulting in loss of vertical support.

42 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Failure Modes ofExterior Truss Seats for Horizontal Tensile Force: The failure of exterior truss seats subjected to a horizontal tensile force can occur in the following modes: (1) fracture of the groove weld

between the gusset plate and spandrel, (2) fracture of the fillet weld between the gusset plate and the truss top chord, (3) tensile fracture of the gusset plate, and (4) shear failure of the bolted connection by bolt

shear, bolt bearing, tear-out, and block shear. For calculation purposes, the bolts were assumed to be

centered m the slotted holes. The typical failure sequence of the exterior truss seat was as follows: (1) the

gusset plate yielded, (2) the groove weld fractured, (3) the truss bearing angle slid so that the bolts were

bearing against the slotted holes and then the bolts sheared off, and (4) the truss walked off the seat angle.

The travel distance for the truss to walk off the seat angle was 4 5/8 in. This failure sequence is illustrated

in Fig. 5-5 as path (A). The relationship between the tensile force resistance and the truss travel distance

is plotted in Fig. 5-6 for path (A) in Fig. 5-5. In this figure, frictional resistance between the seat angle

and bearing angle was not included.

Seat details 1212 and 1313 had a wider gusset plate and followed path (D), where the bolts bore against

the slotted hole then sheared off before the gusset plate connection failed. The failure sequence of seat

detail 1013 was temperature-dependent. At temperatures below 100 °C, the fillet weld connection

between the gusset plate and the truss top chord fractured before the bolts sheared off. At temperatures

greater than or equal to 100 °C, the failure sequence was the same as that for Details 1212 and 1313.

Failure Modes ofInterior Truss Seats for Horizontal Tensile Force: The failure of interior truss seats subjected to a horizontal tensile force can occur in the following modes: (1) shear failure of the bolted

connection by bolt shear, bolt bearing, tear-out, block shear, and (2) fracture of fillet weld connection

between the truss seat and the channel beam. Calculations showed that the bolt shear strength controlled

the truss seat capacity. Bolt shear by itself, however, did not cause the truss to lose its vertical support,

NISTNCSTAR 1-6C, WTC Investigation 43
Chapter 5

but it was the prerequisite to the truss walking off the seat. The travel distance required for the truss to walk off the seat was 4 in.

Yielding of gusset

plate

(A

H

(C)

Fracture of

groove weld

between

gusset plate

and spandrel

Fracture of

gusset plate

Fracture of

fillet weld

between

gusset plate

and top chord

Shear failure of bolts

Shear failure of bolts

Fracture of

fillet weld

between

gusset plate

and top chord

Truss walkoff the seat

(A) Seat details 1 3 11 , 1 4 1 1, 1 5 11 , and 1 6 1 1 at all temperatures.

(B) Seat detail 1111 at all temperatures.

(C) Seat detail 1013 at temperatures below 100 "C.

(D) Seat details 1212 and 1313 at all temperatures, and detail 1013 at temperatures more than or equal to 100 "C.

Figure 5-5. Failure sequence of the exterior truss seats against tensile force.

44 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

140

Groove weld fractures

At travel distance 4-5/8 in. truss walks off support

Bolt shears off

Slip resistance from

bolt connection —

0.2 0.4 Truss travel distance (in)

—I

0.6

20T-2qoic

300"C 4000 "C

500"C

600 T

700"C -

0.8

Figure 5-6. Capacity of exterior truss seat for tensile force (Path (A) in Fig. 5-5 for Detail

1411).

Failure Modes ofExterior Truss Seats for Horizontal Compressive Force: The concrete slab above the

truss seat connection provided the compressive force resistance. In the absence of the concrete slab, the

truss seat resistance against compressive force was provided by the gusset plate until it buckled, and by

bolt shear when the bolt bore against the slotted hole. Surface friction between the seat angle and bearing

angles also provided some resistance. Additional resistance developed when the truss came into contact with the spandrel. Travel distance for the truss to contact the column spandrel was 1 1/2 in. Under

compressive force, the truss did not lose its vertical support.

Failure Modes ofInterior Truss Seats for Horizontal Compressive Force: The reinforced concrete slab

above the truss seat connection provided the compressive force resistance. In the absence of the concrete

slab, the truss seat resistance against compressive force came from surface friction between the seat horizontal plate and bearing angles. Additional resistance was developed when the truss came into contact with the channel beam. Travel distance for the truss to contact the channel beam was 1/2 in. Under compressive force, the truss did not lose its vertical support.

Failure Modes ofInterior and Exterior Truss Seats for Combined Vertical and Horizontal Forces: The

failure modes of the interior and exterior truss seats when subjected to combined vertical and horizontal

forces were a combination of the failure modes for vertical and horizontal forces. The vertical shear

strengths of fillet welds in both the interior and exterior truss seats were reduced by the horizontal tensile

force. This fillet weld was between the vertical plate and channel beam for interior truss seats and

between the stand-off plate and spandrel for exterior truss seats. The horizontal tensile strengths of the

truss seats were not reduced by the additional vertical forces on the truss seats.

NISTNCSTAR 1-6C. WTC Investigation 45
Chapter 5

5.2.4 Truss Seat Capacity Calculations

In this section, truss seat capacities corresponding to the failure modes described in the previous section

are given. The capacities were computed for different types of truss seats at different temperatures.

Calculation of the capacities was performed using the methods in the Manna! ofSteel Construction: Load

and Resistance Factor Design (AISC 2001 ) with the resistance factor, (/>, assumed to be equal to one.

Capacity ofExterior Truss Seats for Vertical Force: The failure mode of the truss seat against vertical force was fracture of the fillet welds at the stand-off plate to spandrel connection. Strength of the fillet welds at this connection is summarized in Table 5-2 and Fig. 5-7. The symbol # in this table refers to seat detail number.

Capacity ofInterior Truss Seats for Vertical Force: Failure mode of the truss seat against vertical force was fracture of the fillet welds between the seat vertical plate stiffener and channel beam. Strengths of

the fillet welds at this joint are summarized in Table 5-3 and Fig. 5-7.

46 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Table 5-2. Exterior truss seat capacity for vertical force.

Temp.

CQ

Connection Detail Capacity' for Vertical Force (kip)

#1013 #1111 #1212 #1311 #1313 #1411 #1511 #1611

20 94 94 111 94 94 140 193 207

100 94 94 111 94 94 140 193 207

200 93 93 110 93 93 139 192 206

300 91 91 108 91 91 136 187 201

400 84 84 100 84 84 126 172 184

500 69 69 81 69 69 102 136 146

600 45 58 53 60 45 78 84 90

700 29 26 34 27 29 35 38 41 800 14 13 17 13 14 17 19 20

900 12 11 14 11 12 14 16 17 1000 12 11 14 11 12 14 15 17

Table 5-3. Interior truss seat capacity for vertical force.

Temp.

CO

Connection Detail Capacity for Vertical Force (kip)

#15 #17 #20 #21 #22 #23 #226A

20 233 233 274 229 194 194 395

100 233 233 274 229 194 194 395

200 232 232 273 228 194 194 393

300 226 226 267 223 189 189 384

400 207 207 244 204 173 173 352

500 164 164 194 162 137 137 279

600 101 101 119 100 85 85 172 700 46 46 54 45 39 39 78

800 23 23 27 22 19 19 38

900 19 19 22 18 16 16 32

1000 19 19 22 18 16 16 32

NISTNCSTAR 1-6C, WTC Investigation 47
Chapter 5

I n

1»3 1 n n 20C 400C 600C 700C

#1411

20C 400C 600C 700C #1511

20C 400C 600C 700C #1311

20C 400C 600C 700C #20

20C 400C 600C 700C #226A

20C 400C 600C 700C #15 and #17

91 84

Orieinal document reproduced with permission of The Port Authority of New York and New Jersey.

Figure 5-7. Truss seat capacity for vertical force

48 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Capacity ofExterior Truss Seats for Horizontal Tensile Force: The capacities of truss seats that followed failure sequence (A), as shown in Fig. 5-5, were governed by the fracture strength of the groove

weld between the gusset plate and the spandrel. The capacities of truss seats that followed failure sequence (B) were governed by the tensile fracture strength of the gusset plate, and truss seats that followed failure sequence (C) were governed by the fracture strength of the fillet weld between the gusset

plate and the truss top chord. The capacities of truss seats that followed failure sequence (D) were

governed by a combination of shear strength of bolts and tension developed in the gusset plate. The

results of the exterior truss seat capacity calculations are summarized in Table 5-4 and Fig. 5-8. Note

that the strength of the truss seat #1013 at 100 °C is higher than that at 20 °C by about 38 percent. For

temperatures less than 100 °C, the capacity was controlled by the fillet weld strength, and for temperatures in excess of 100 °C, the bolt reached the end of its travel in the elongated bolt hole, thus

providing a stiffer load path and higher load capacity of the connection.

Capacity ofInterior Truss Seats for Horizontal Tensile Force: Failure loads were computed for the

failure modes described above, including shear failure of the bolted connection by bolt shear, bolt bearing, tear-out, block shear, and fracture of fillet weld connection between the truss seat and the

channel beam. The results showed that the shear strength of the two bolts controlled the horizontal tensile

strength of the truss seat connection for all seat details including 15, 17, 20, 21, 23, and 226 A. Table 5-5

and Fig. 5-8 summarize the capacities of interior truss seats for horizontal tensile force. As can be seen from this table, at temperature 500 °C, bolt shear capacity was reduced by half, and at 600 °C it was

reduced to less than a quarter of the original capacity at room temperature.

Capacity ofExterior Truss Seats for Horizontal Compressive Force: Under compressive force, the

gusset plate buckled before the bolts sheared off Compression strength of the gusset plate governed the

exterior truss seat capacity. The compressive strength of gusset plate is summarized in Table 5-6.

Capacity ofInterior Truss Seats for Horizontal Compressive Force: Under compressive force, the truss came into contact with the channel beam before the bolt bore against the slotted hole. The interior truss seat did not fail under compressive force.

Capacity ofInterior Truss Seats for Combined Vertical and Horizontal Force: A typical interaction

relationship for the combined vertical and horizontal tensile force is shown in Fig. 5-9.

NISTNCSTAR 1-6C, WTC Investigation 49
Chapter 5

Table 5-4. Exterior truss seat capacity for horizontal tensile force.

Temp.

CO

Connection Detail Capacity for Horizontal Tensile Force (kip)

#1013 #1111 #1212 #1311 #1313 #1411 #1511 #1611

Fracture of

Fillet Weld/

Shear Failure of Bolts

Fracture of

Gusset Plate

Shear Failure of BoltsFracture of

Gi oove Weld

Shear Failure of BoltsFracture of Groove WeldFracture of Groove WeldFracture of Groove Weld

20 100 104 182 126 182 126 126 126

100 138 104 181 126 181 126 126 126

200 135 103 180 126 180 126 126 126

300 130 101 174 123 174 123 123 123

400 115 93 156 113 156 113 113 113

500 84 75 117 91 117 91 91 91 600 42 49 67 58 67 58 58 58

700 20 25 32 30 32 30 30 30

800 14 16 19 18 19 18 18 18 900 13 14 17 16 17 16 16 16 1000 13 14 17 16 17 16 16 16

Table 5-5. Interior truss seat capacity

against horizontal tensile force.

Temp.

CO

Capacity (kip)

Shear Failure of

Bolts 20 44

100 44

200 44

300 42

400 34

500 21 600 9 700 4

800 4

900 4

1000 4

50 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Original document reproduced with permission of The Port Authority of New York and New Jersey.

Figure 5-8. Truss seat capacity for horizontal tensile force.

NISTNCSTAR 1-6C, WTC Investigation 51
Chapter 5

Table 5-6. Compression strength of gusset plate.

Temp.

(°C)

Compression Strength of Gusset Plate (kip)

#1013 #1111 #1212 #1311 #1313 #1411 #1511 #1611

20 74 68 98 90 98 90 90 90

100 71 66 95 86 95 86 86 86

200 68 63 90 82 90 82 82 82

300 65 60 86 78 86 78 78 78

400 60 55 79 72 79 72 72 72

500 46 42 60 55 60 55 55 55 600 19 17 25 22 25 22 22 22

700 6 5 8 7 8 7 7 7 800 6 5 7 6 7 6 6 6 900 6 5 7 6 7 6 6 6 1000 6 5 7 6 7 6 6 6

200

50

Horizontal tensile strength (kip)

Figure 5-9. Capacity of interior truss seat against vertical and horizontal force

(for Detail 22).

52 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.2.5 Modeling Failure by Break Elements

In this section, the finite element models developed to capture failure modes of the exterior and interior truss seats, studs on strap anchors, and studs on spandrels are described. These models were developed

for incorporation in the floor truss analysis to capture the connection failure modes, failure loads as a function of temperature, and failure sequences.

The models of these connections simulated the loss of connection resistance after their failure either from

exceeding the connection force capacity or from exceeding the allowable deformation (for example, truss walking off the seat). The connection capacity was also temperature-dependent. The finite element

modehng assumptions are as follows:

A control element (COMBIN37), a unidirectional linear spring element with the capability of turning on

and off during an analysis, was used for modeling connection failure. The element is referred to as "break

element" in this report. The element is a part of the structure that connects two "active" nodes in the "on"

mode and disconnects them in the "off mode, depending on the relative displacement of two "control"

nodes. The break element is defined as follows:

B.,[{iJ,dof,,);{k,l,dofi,i);iKJo)] (12)

where m is the break element number, / andj are the active nodes, dofij is the degree of freedom for the

active nodes, k and / are the control nodes, dofi;i is the degree of freedom for the control nodes, K is the

elastic stiffness of the break element, and Ao is the differential displacement hmit of the control nodes.

To make the connection capacity temperature-dependent, a beam element with temperature-dependent

coefficient of thermal expansion was added to the break element. This was done by using the

deformation of a beam element from thermal expansion to control the status (on/off) of the break element.

Figure 5-10 illustrates the basic mathematical model of the connection using break elements.

Multiple connection failure modes require use of different break elements that are connected together in a

logical manner. For example, to model independent failure modes, that is, one failure mode that does not cause other failures, break elements are connected in parallel so that when one break element turns "off,

the other break elements remain "on". For dependent failure modes, break elements are connected in series so that when one break element turns "off, all elements turn "off.

NISTNCSTAR 1-6C, WTC Investigation 53
Chapter 5

Basic mathematical model:

- Let node / and / have same displacement.

- In this example, control nodes k and / relative displacement has the form:

U,-U,= — + oLAT

- Break element status is by definition

U,. - U, < , status : on - UI > Af), status : off

P W. I .

J k

Break element Beam element

P. - Define break element to turn off when capacity, P,„ has been reached

K p

Element capacity at room temperature is given as

- Hence for a given P,, and AT relationship, the required thennal expansion to turn the break element

off can be found by

a = PII. nil -Pii_ KLAT

- Stiffness, K Lenslh. L

Status: off <

Figure 5-10. Basic mathematical model of connection failure.

54 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.2.6 Summary of Failure Modes and Finite Element Models of Truss Seats

The failure modes of the interior truss seats include (I) truss walking off the seat, (2) exceeding the

vertical temperature-dependent shear capacity of the fillet welds between the seat vertical plate stiffeners and channel beam, and (3) exceeding temperature-dependent shear capacity of bolts when they bear

against the slotted holes. These failure modes were modeled by using four break elements and two beam

elements as shown in Fig. 5-11. The interior seat model was tested in ANSYS, and resuhs are shown in Figs. 5-12 and 5-13. These figures depict the relationship between the horizontal and vertical seat forces

and the horizontal truss travel distance.

Figure 5-12 shows the results from analysis where the truss seat was subjected to a constant vertical load

and horizontal displacement increments at 500 °C. When a truss seat is subjected to a large horizontal

tension and small vertical shear, the failure is by two bolts shearing off followed by the truss walking off

the seat, as shown in Fig. 5-12. The shear strength of the bolts controls the truss seat horizontal tension

capacity. The bolt shear by itself does not cause the truss to lose its vertical support, but it is the

prerequisite for the truss walking off the seat. The travel distance for a truss to walk off a truss seat is 4 in. for an interior seat and 4 5/8 in. for an exterior seat.

Figure 5-13 shows the results from analysis where the truss seat was subjected to a constant horizontal

load and vertical displacement increments at 500 °C. When a truss seat is subjected to a large vertical

shear and small horizontal tension, the failure is by the fracture of fillet welds between the vertical plate

stiffeners and the channel beam at an interior seat and between the stand-off plates and the spandrel at an

exterior seat, resulting in loss of both vertical and horizontal support, as shown in Fig. 5-13.

The finite element models of the exterior truss seats were similar to those for the interior truss seats, except for an additional beam element and a break element to model failure of the gusset plate, as shown

in Fig. 5-14.

NISTNCSTAR 1-6C, WTC Investigation 55
Chapter 5

Beam element Rigid beam

Rigid beam

Seat model was used to make the

connection between node /?/, which is part of the seat and channel beam, and

node rij, which part of the floor truss. The seat model consists of four break

elements, two beam elements, and six

nodes.

Beam element

(Out-of-plan)

Break element No. 1 : Capture walk-off support

B,[(2,3.UZ);(2,l.UY);(K,An)]

Break element No. 2: Capture seat vertical shear capacity

B:[( 1 ,3,UZ);(4,2,UZ);(K,An)]

Beam element No. 1: Make seat vertical shear

capacity temperaturedependent

Beam element No. 2: Make bolt shear capacity

temperature-dependent

Constraint equations

Coupling displacement

DOF of node 1 and 6

Break element No. 3:

Capture loss of horizontal

resistance if seat fails vertically

B3[(2,3,UY);(4,2.UZ);(K,Ao)]

Break element No. 4:

Capture bolt shear capacity

B,[(l,3,UY);(2,5,UY);(K,Ao)]

Beam element

(Out-of-plan)

-f Z

Coordinate system

Figure 5-11. Representation of interior truss seat by break elements.

56 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

25

Bolts shear off

Horizontal Resistance

Vertical Resistance

Truss walks off the seat Seat continues to provide | vertical resistance until [ truss walks off the seat l

1

1 2 3 Truss Travel Distance (in.

Figure 5-12. Results of interior truss seat model capturing failure

from truss walking off the seat at 500 °C.

160

140 a 120

g 100 o

LL

0)U

c

•Horizontal Resistance

Vertical Resistance

80

60

(/) q: 40

20 -

0

0.0 0.2 0.4 0.6 0.8 1.0 Applied Vertical Load / Vertical Shear Capacity

Shear vertical shear failure

Loss of horizontal

resistance due to seat vertical shear

failure

1.2

Figure 5-13. Results of interior truss seat model capturing failure

from exceeding the vertical shear capacity at 500 X.

NISTNCSTAR 1-6C, WTC Investigation 57
Chapter 5

Exterior column

centerline

Exterior seat model same as the

interior seat

Gusset plate connection model was used to make the connection between node rii, which is part of the column/spandrel, and node n^, which

is part of the floor truss. The connection model

consists of one break element, one beam

element, and four nodes.

Beam element: Make gusset plate tensile strength

temperature-dependent

Break element:

Fix rotational DOF

Constraint equations

Coupling displacement DOF of node 1 and 3

Capture failure of gusset plate under tensile force

B,[(1.2.UY);(4,2.UY);(K,Ao)]

Y

AZ

Coordinate system

58

Figure 5-14. Representation of exterior truss seat by break elements.

NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.2.7 Summary of Failure Modes and Finite Element Models of the Stud on Strap

Anchor and Spandrel Stud

Stud on Strap Anchor: There were four 5/8 in. x 2.5 in. studs on each strap anchor as shown in Fig. 5-15. Calculations were carried out to compute the lateral shear capacity of these stud shear connectors using the procedure in Building Code Requirementsfor Structural Concrete (ACI 318-02) at different temperatures. The following failure modes were considered in the calculation: steel shear

failure, concrete pryout, and concrete breakout. The capacity of the stud close to the edge of the slab was

governed by concrete breakout at all temperatures, while those of the other three studs located farther from the concrete edge were governed by concrete pryout at temperatures below 700 °C and steel shear

failure at temperamre equal to and above 700 °C.

Spandrel Stud: There was one 3/4 in. x 6 in. spandrel stud located between two adjacent exterior columns

as shown in Fig. 5-15. Calculations were carried out to compute the shear capacity and tensile capacity

of the spandrel stud at different temperatures. For shear capacity, the following failure modes were

considered: steel shear failure, concrete pryout, and concrete breakout. For tensile capacity, the following

failure modes were considered: steel tensile failure, concrete breakout, pullout strength, and concrete sideface blowout. The shear and tensile capacities of the spandrel stud were both governed by concrete breakout strength.

Finite element models of studs on strap anchors and studs on spandrels were developed using break

elements. The stud model included 8 break elements and 4 beam elements, as shown in Fig. 5-16.

Figure 5-15. Location of stud on strap anchor and spandrel stud.

NISTNCSTAR 1-6C, WTC Investigation 59
Chapter 5

Four beam elements were used to make the stud shear connector temperature-dependent

- Node on slab

- Node on spandrel

Constraint equations

Coupling displacement

DOF of node 1 and 10

Break element No. 4: Capture loss of lateral resistance

in the Y direction if failure occurs

in the negative X direction

B4[(2,5,UY);(8,2,UX);(K,Ao)]

Break element No. 3: Capture loss of lateral resistance

in the Y direction if failure occurs

in the positive X direction

B3[(4,5,UY);(2,6,UX);(K,Ao)]

The purpose of break elements No. 5-8 is similar to break elements No. 1-4

Break element No. 1: Capture lateral shear failure in the positive Y direction

B,[(l,3,UY);(2,7,UY);(K,Ao)]

Break element No. 2: Capture lateral shear failure in the negative Y direction

B2[(3,4,UY);(9,2,UY):(K,Ao)]

Figure 5-16. Representation of stud shear connector by break elements.

60 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.3 KNUCKLE ANALYSIS

The objective of this analysis was to predict the capacity of the knuckle subjected to loads between the

truss and the concrete slab and to develop a finite element model of the knuckle to be included in the full floor subsystem model.

5.3.1 Description of Knuckle

The "knuckle" was formed by the extension of the truss web diagonals into the concrete slab. It provides

for composite action of the steel truss and concrete slab (see Fig. 2-1) as it allows shear transfer in both

the transverse and longitudinal directions.

5.3.2 Failure Modes of Knuckle

Failure modes of knuckles are:

• Horizontal shear failure due to crack or crushing of concrete

• Pullout failure due to vertical tension

5.3.3 Knuckle Shear Tests

Two sets of experiments were performed in 1967 at Laclede Steel Company in Saint Louis, Missouri, to determine the transverse and longitudinal shear capacities of the knuckle.

The longitudinal shear test consisted of double knuckles cast into two concrete blocks as shown in Fig. 5-17. The test specification showed comer angles confining the concrete blocks and no

reinforcement in concrete. However, the test pictures showed reinforcement in both directions for each

concrete block, with the comer angles dismantled. The test specification called for concrete density of

152 pcf, which corresponds to a normal weight concrete. The slab in the office areas was made from

lightweight concrete. Three specimens were tested: two specimens after 28-day curing and one after 96-day curing. The average compressive strength of two 28-day cylinders tested was 4,290 psi. A third

sample, tested after 96 days, showed a strength of 2,850 psi. No reason is known for the compressive

strength in the third test being less than the other two tests. The test specification did not identify the weld size connecting the inner ends of the two knuckles to two channels. However, the primary failure mode observed in the third test was weld failure. Weld failure was not identified as the failure mode of

the knuckle for the other two tests. The results of the longitudinal shear strengths of the knuckle based on

the first two tests were approximately 28.3 kip per knuckle. The strength of in-place, mature, lightweight concrete is 4,100 psi, and the 28-day corrected average strength of the normal weight concrete used in the

test was 3,707 psi. After adjusting for the strength of in-place, mature, lightweight concrete by

multiplying by the ratio of 4,100 psi to 3,707 psi, the longitudinal shear capacity of the knuckle in the

WTC floor systems was determined at approximately 3 1 kip per knuckle.

The transverse shear test consisted of double knuckles cast into two reinforced concrete blocks that were

confined at the comers by angles as shown in Fig. 5-18. The concrete density was 110 pcf,

corresponding to a lightweight concrete. Two tests were conducted, seven and 27 days after casting

concrete. The concrete compressive strengths reported for seven-day and 27-day cylinder tests were

1,330 psi, and 2,600 psi, respectively. The inner ends of the two knuckles were connected through

channels to a #1 1 rebar, and the rebar was loaded until the concrete failed. The tests were conducted at concrete ages of six and 27 days. The primary failure mode observed was concrete shear failure. The

pictures from the tests showed formation of a shear crack in one of the concrete blocks. The transverse

NISTNCSTAR 1-6C, WTC Investigation 61
Chapter 5

shear capacity of the knuckle, as the average of the two reported tests, was 16.9 kip per knuckle. For the WTC floor system, the knuckle transverse shear capacity was determined by adjusting the strength of in- place, mature, lightweight concrete of 4,100 psi relative to the average strength of the lightweight concrete used in the test of 1,965 psi. Multiplying by the ratio of 4,100 to 1,965 psi, the transverse shear

capacity of the knuckle in the WTC floor system was determined at approximately 35 kip per knuckle

:J

iTM—

1

j Se^CiO'^ faint SKfj^J(VS noims. 'n«Kt^

i - (I r^^^.....^ -.wTMTMTMTM— ^

J fit iio .gs?^ wftid tr«*«

rfOK? ^-f. I Stea!" Test;

1 j gSSi

-I

,

^ 'v f-'. ttaEj^irg?. Tcstlftg :.&!>CEy«tc i '~"r«r, ESA*.'^^ nttfm *

Infonnation provided by Laclede Steel

Figure 5-17. Longitudinal shear test of a knuckle.

62 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Information provided by Laclede Steel

Figure 5-18. Transverse shear test of a knuckle.

5.3.4 Finite Element Model for Knuckle Test

The LS-DYNA computer program was used for the analysis. Finite element models, shown in Fig. 5-19,

represent one quarter of the knuckle test specimens. The knuckle and channel members in the test set-up were modeled with solid elements with steel material properties. Concrete was also modeled with solid

elements with the Pseudo Tensor material model described in Chapter 3. Two different assumptions were made about the interface condition between the concrete and the steel, namely, fully bonded or

frictionless. Boundary conditions are also shown in Fig. 5-19. Displacement was imposed in a form of a ramp to the angles.

5.3.5 Material Properties for Knuckle Analysis

The concrete strengths used in the finite element model were 4,100 psi for the longitudinal shear test and

2,500 psi for the transverse shear test. In addition, 0.47 percent steel reinforcement, representing the

welded wire reinforcement of the slab, was added in a distributed way to the concrete.

Angles were modeled with Material 21 (see Chapter 3 for description).

NISTNCSTAR 1-6C, WTC Investigation 63
Chapter 5

UZ=0

(top edge of angle

UX=0

Plane of symmetry

UZ=0

(2.1 in. region along base -

simulating support bracket)

(a) Longitudinal sheat test model

UZ=0

(top edge of angle)

UYmax=0.30 in.

••w^ UY=0

(b) Transverse sheat test model

UXmax=-0.10 in. (applied to all nodes on

the end face of angle)

UZ=0

(2.1 in. region along base -

simulating support bracket)

Plane of symmetry

Figure 5-19. Finite element models of knuckle shear tests.

5.3.6 Results from Knuckle Analysis

Finite Element Analysis (FEA) of Tests

The results of FEA of the tests are shown in Figs. 5-20 through 5-23. The resuUs showed significant

dependence on the interface characteristics between the steel and the concrete. The results of FEA of the

longitudinal shear test (Fig. 5-21) showed that each knuckle had strength in the range of 15 kip to 35 kip,

depending on the interface condition. When the analysis results are compared to the test results, the

interface appears to be closer to the fully bonded case. The transverse shear FEA results (Fig. 5-23) showed that transverse knuckle strength was about 24 kip

for the frictionless condition with 2,500 psi concrete, which corresponds to 39 kip for 4,100 psi concrete. For the full bonded case, the analysis was terminated at 20 kip per knuckle before reaching the ultimate

64 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

strength. The transverse shear FEA results (Fig. 5-22) showed that concrete was crushed in a small

region next to the knuckle and extended in front of the shear load. Figure 5-22 also shows large regions

of crushed concrete at the lower portion of the model. (Note that the boundary condition UY=0, although

realistic for the test, would not occur in a pair of transversely loaded knuckles in the two actual trusses.)

The small crushed regions indicate that a pair of knuckles can be expected to behave nearly independently

of each other and, therefore, have nearly double the capacity of a single knuckle.

Although the analysis showed the sensitivity of the results to the steel-concrete interface assumptions, it supported the shear capacities determined from test results.

VaOii, SC&vTJOS

Figure 5-20. Compressive stresses in longitudinal shear finite element model

(4,100 psi concrete).

80000

uu

o

70000-

60000

5000O

40000

30000

2000O

lOOOfr

0

1 Aim

I-

•

—^ 0 Friction Contact

Fully Bonded ; -^h^—

~w

\

0.00 0.02 0.04 0.06 0.08 Displacement (in.)

0.10 0.12

Figure 5-21 . Shear force versus displacement from finite element model

for longitudinal shear of two knuckles (4,100 psi concrete).

NISTNCSTAR 1-6C, WTC Investigation 65
Chapter 5

ijn^iaL—. — " mm

-itw -r',: m.nt

Figure 5-22. Compressive stresses in transverse shear finite element model

(2,500 psi concrete).

50000

45000

40000

35000 « 30000

25000

20000

15000

10000

5000

if

If —0 Friction Contact

Fully Bonded

0

0.00 0.05 0.10 0,15 0.20 Displacement (in.)0.25 0.30

Figure 5-23. Shear force versus displacement from finite element model

for transverse shear of two knuckles (2,500 psi concrete).

Analysis of Temperature Effects

Temperature effects on knuckles were evaluated based on hand calculations and engineering judgment.

The effects can be summarized as follows:

• The steel knuckle heated rapidly and reached the temperature of the truss web diagonal

member without much loss of heat into the relatively cool concrete slab. Concrete had a low

coefficient of conductivity and did not respond as rapidly as steel to the rise of temperature.

• Concrete in the immediate proximity of the steel knuckle heated to a temperature close to that of the steel.

• Shear failure of the knuckle was initiated by the failure of concrete in close proximity to the

knuckle. Final failure engaged not only the hot concrete in close proximity to the knuckle,

but the cooler concrete farther away.

66 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

• It was assumed that for gas temperatures of 20 T to 450 °C, 650 °C, 850 °C, and 1 ,050 X,

the knuckle steel temperatures would be lower at 20 T to 375 T, 550 T, 725 T, and

900 °C, and average concrete temperatures would be even lower at 20 °C to 300 T, 450 °C,

600 °C, and 750 °C, respectively.

Neglecting the difference in thermal expansion of concrete and steel, for gas temperatures of 20 °C to 450 °C, 650 °C, 850 °C. and 1.050 °C, the expected concrete strength at the knuckle is in the range of

4,100 psi, 3,300 psi, 2,600 psi, and 2,000 psi based on the expected concrete temperature. Based on the

results of tests performed and bracketing of test results by the finite element analysis, the knuckle

capacities in either longitudinal or transverse direction are 30 kip, 24 kip, 19 kip, and 15 kip for the

average concrete temperature of 20 °C to 300 °C, 450 °C, 600 °C, and 750 °C, respectively. Temperaturedependent knuckle shear capacities for the assumed temperatures are summarized in Table 5-7.

For the pullout failure mode, the capacity was estimated at 15 kip at room temperature. Based on

concrete temperature and concrete strength, temperature-dependent capacity for pullout was calculated as shown in Table 5-7.

Table 5-7. Temperature-depend ent knuckle capacity for assumed temperatures.

Gas temperature

CO

Steel temperature

CC)

Concrete

temperature

(°C)

Knuckle shear

capacity

(kip)

Knuckle pullout

capacity

(kip)

20-450 20 - 375 20 - 300 30 15 650 550 450 24 12 850 725 600 19 10

1.050 900 750 15 7

5.3.7 Summary of Failure Modes and Finite Element Models of Knuckle Model for

Truss Model

Knuckle failure modes captured by the finite element models of knuckles in the truss model were the

horizontal shear failure and vertical tensile pullout failure, which are both temperature-dependent. Finite

element modeling assumptions for the knuckle are: (1) the knuckle has resistance in all translational

degree of freedom. (2) the knuckle does not have a vertical compression capacity limit, (3) capacities in the horizontal shear and vertical tension are temperature-dependent, and (4) vertical compression

resistance is independent of the capacities in the other directions. A finite element knuckle model was

constructed by using 1 5 break elements and five beam elements for incorporation into the truss model, as shown in Fig. 5-24.

NISTNCSTAR 1-6C, WTC Investigation 67
Chapter 5

fl~, - Node on slab

Five beam elements are used to make the knuckle

capacity

temperature-dependent

Point-to-point contact element to transfer

vertical compressive force between node 1 and 2

Constraint equations

Coupling displacement

DOFofnode 1 and 7

Break element No. 1-4: Capture loss of vertical resistance if knuckle fails horizontally

B,[(2.6.UZ);(8,2,UX);(K,Ao)]

B:[(6,5,UZ);(2,9,UX);(K,Ao)]

B3[(5,4,UZ);(10,2,UY);(K,Ao)]

B4[(4,3,UZ);(2,ll,UY);(K,Ao)]

Break element No. 5: Capture knuckle tensile failure

B,[(3,l,UZ);(12,2,UZ);(K,An)l

^r^A \ \ \ F

Break element No. 10: Capture loss of horizontal

resistance in the Y direction if knuckle fails vertically

B,o[(2,6,UY);(12,2,UZ);(K,Ao)]

The purpose of break elements No. 11-15 is similar to break elements No. 6-10

Break element No. 8-9: Capture loss of horizontal

resistance in the Y direction if knuckle fails horizontally in the X

direction

Bh[(5,4,UY);(8.2,UX);(K,Ao)]

Bg[{6.5.UY);(2.9.UX);(K.Ao)]

Break element No. 6: Capture knuckle horizontal compression failure in the Y direction

B,[(3.1,UY);(10,2,UY);(K,Ao)]

Break element No. 7: Capture knuckle horizontal tensile

failure in the Y direction

B7[(4.3,UY);(2,ll,UY);(K,Ao)]

Figure 5-24. Representation of knuckle by break elements.

68 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.4 TRUSS MODEL

The truss model is a section of a floor system, which consists of a single floor truss and a corresponding

section of the concrete slab. The objectives of the truss model study were to:

• Capture the potential failure modes and failure sequence of the truss model subjected to gravity load and temperature time histories,

• Determine failure loads for different failure modes, and

• Develop a simplified model that replicates the expected failure modes of the truss model for use in the full floor subsystem model.

5.4.1 Model Description

Figure 5-25 shows the truss model. The truss model is a cut-out section of the office area floor system.

A typical long-span truss designated C32T1 (SHCR 1973:WTC Drawing Book 7, Sheet ABl-2) was

modeled. The model used symmetry and included the following:

• One of the two primary trusses at Column 143 at Floor 96 of WTC 1,

• Two exterior columns (Columns 143 and 144) at the plane of symmetry with half the area and the moment of inertia and with a length of 24 ft (each column extends over the fijll height

of a floor),

• Part of the spandrel between the two planes of symmetry,

• Part of the slab (40 in. wide) between the two plane of symmetry,

• Strap anchor attached on one end to the truss top chord and the concrete slab and on the other

end to the adjacent exterior column (Column 144), and

• Halves of exterior and interior truss seats and the gusset plate at the exterior end.

The slab was 4 in. thick hghtweight concrete on 22 gauge steel deck with flutes 6.8 in. on center running

parallel to the primary trusses. Two layers of welded wire reinforcement were provided in the slab. The

reinforcement ratios were 0.21 percent and 0.735 percent in the directions parallel and transverse to the

truss, respectively. A flute was 2 in. wide at the top, 1.25 in. wide at the bottom, and 1.47 in. high.

The finite element model of the concrete slab had an equivalent thickness of 4.35 in. By using the

equivalent thickness, the bending stiffness in the direction transverse to the truss became about 15 percent

higher than the actual stiffness. However, since the bending in the transverse direction to the truss was

small, the concrete slab was modeled as an isotropic plate. The steel deck and the welded wire fabric were not included in the truss model either explicitly or implicitly by modification of concrete stress- strain relationship. The concrete slab was modeled with four layers of 3-D eight-node structural solid

(SOLID 185) elements. The Hjelm plasticity model as described in Section 3.1.2 was used for the solid

elements that allowed different "yield strengths" in tension and compression.

The top chord of truss C32T1 consisted of double angles of 1 1/2 x 2 x 0.25 (long legs horizontal), and

the bottom chord consisted of double angles of 3 x 2 x 0.37 (long legs horizontal). Web diagonal

members were round bars of either 1.09 in. or 1.14 in. diameter. Most web diagonal members had a

1 .09 in. diameter.

The top and bottom chords and the vv-eb diagonals were modeled by BEAM 189 elements with

temperature-dependent elastic, plastic, and creep material properties. Top and bottom chords were

NISTNCSTAR 1-6C, WTC Investigation 69
Chapter 5

divided into four elements between panel points; panel points are those where web diagonals attached to chord members. Web diagonals were also divided into four elements between top and bottom chords.

288 in.

i

V <

\/\/\/\/\/\/' 'TsK.

span=713 in.

(a) Entire model

40 in knuckle

top chord

29 in.

(b) Cross section

bottom chord

(c) Top and bottom chords and web diagonals

Figure 5-25= Truss model.

At knuckle locations, elements representing the top chord and the concrete slab were connected by break

elements (COMBrN37) with capacities determined from the knuckle analysis. By including point-topoint contact (CONTA178) elements, compression was transferred even after failure of knuckles. The

studs on the strap anchor between the top chord and column 144 were also modeled by break elements

(COMBIN37) that connected the strap anchor to the slab and had temperature-dependent capacities. The

slab and the strap anchor were tied by the COMBIN37 break elements horizontally while their vertical

displacements were coupled. The exterior and interior truss seats were modeled by COMBrN37 break

elements that had temperature-dependent capacities determined from the truss seat analysis. A stud on

the spandrel was also modeled by COMBIN37 break elements, which tied the spandrel with the slab and

had temperature-dependent capacities.

The visco-elastic damping unit that connected the truss bottom chord to the spandrel plate was not included in the truss model because the dampers were expected to be soft when subjected to very slow

loading rates.

70 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Elastic BEAM44 elements were used to model the exterior columns. Elastic SHELL63 elements were

used to model the spandrel.

A camber of 2.0 in. at midspan was not included in the truss model.

5.4.2 Failure Modes

Two possible failure modes were identified for the truss model:

Sagging of Truss: The top and bottom chords and web diagonals were exposed to the hot gas layer that accumulated below the floor slab. The steel in the truss exhibited stiffness degradation, yield strength

reduction, plastic softening, and creep at high temperatures. A truss with softened chords and diagonals

would sag. As the concrete slab was heated, its stiffness and strength were reduced, especially at its bottom layer where temperatures were the highest due to exposure to hot gas and around the knuckles

where concrete temperature rose by conduction through the steel.

In addition to direct thermal effects, sagging and weakening of the truss were caused by the following

component failures:

• Buckling of web diagonal members,

• Yielding of the chord members,

• Knuckle failure and loss of composite action between the concrete slab and the steel truss (see Section 5.3), and/or

• Weld failure betv\ een the web diagonal members and the chord members.

Loss of Truss Support: The truss can fail by loss of support. Loss of support at either the exterior or

interior truss seats was caused by the loss of vertical shear capacity of the seats at elevated temperatures

or by the truss walking-off the seat due to large sagging.

As discussed in Section 5.4.3, the bottom chord of the truss model was restrained in the direction transverse to the truss at the bridging truss locations. Although the out-of-plane defonnation of the

bottom chord due to thermal expansion of bridging trusses may result in a reduction of the vertical load

capacity of a primary truss, the use of symmetry in the truss model prevents its application to cases with

lateral loads. The interaction between the bridging trusses and the primary trusses was captured in the full floor model.

5.4.3 Boundary Conditions

Boundary conditions for the truss model are shown in Fig. 5-26.

The entire top chord of the truss was restrained against lateral movement in the x direction. The bottom

chord was restrained against lateral movement in the x direction at four bridging truss locations. The two

edges of the concrete slab parallel to the truss were restrained against rotations about the v and z axes, but were free in the x direction.

The interior truss seat was fixed in all directions. The exterior truss seat was attached to the spandrel.

The truss was supported by break elements to capture failure modes of the truss seats, and break elements were connected to beam elements representing the seats. The exterior end of the slab was tied to the spandrel by contact elements to prevent the slab from

penetrating the spandrel and break elements representing tension and shear failures of the spandrel stud.

NISTNCSTAR 1-6C, WTC Investigation 71
Chapter 5

The interior end of the slab was fixed in the z direction, but connected to break elements with

temperature-dependent tensile capacities of the slab in they direction, as shown in Fig. 5-27. Therefore,

the interior slab end was fixed in the v direction as long as the tensile force was within the tensile capacity

of the slab calculated for the actual steel reinforcement in the region between office area and core slabs

(#3@10 in. top and #4@12 in. bottom).

The top and bottom ends of the columns were restrained against all rotations and against the translation in the j-direction. In addition, the lower columns were restrained against the translation in the vertical

direction. The end restraint conditions of columns affect the magnitude of the horizontal reaction to thermal expansion of the floor section. A quantitative study of the effect of column boundary conditions

is discussed in Section 5.5.16.

Fixed UZ and

UY at the end

Figure 5-26. Boundary conditions.

B-'eak Elements

Figure 5-27. Break elements at the interior end of slab.

72 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.4.4 Loads

Loads on the truss model consisted of dead and live loads and temperature time histories for all truss components including the truss seats and concrete slab. The gravity loads included the weight of the

structure, 8 psf superimposed dead load (including nonstructural dead loads due to architectural items and

fixed service equipment), and 13.75 psf of live load equal to 25 percent of design live load of 55 psf.

A temperature time history was used for exercising the truss model (Figure 5-28). It was not obtained

from fire dynamics or heat conduction analyses. The temperature was ramped over the first 30 min

linearly from 20 °C to 700 °C in truss members, from 20 °C to 700 °C at the bottom surface of the concrete slab, and from 20 °C to 300 °C at the top surface of the concrete slab; thereafter, the maximum

temperatures were linearly increased at a rate of 20 °C per min. At 40 min temperatures increased by

200 °C from those at 30 min. A linear gradient through the thickness of the slab was assumed. No

temperature load was applied to the columns or spandrel.

The effects of construction sequence were included by using "element birth and death" for the concrete

slab. In the first step, the self-weight of truss members and concrete slab was applied to the truss without

the concrete slab. In the second step, the concrete slab was placed stress-free, and the superimposed dead

and live load were applied to the model.

To determine the effect of debris load on the truss behavior, the gravity was increased until the analysis

failed to converge at room temperature.

ZUMZNTS ANSYS 8.0 7=MP£SA~J3£S

FSB 13 2004 18:07:48

^MfJ(-700

1 1 M 1 1 ^"g^

Figure 5-28. Assumed Temperature Distribution in the Truss Model at 30 min.

5.4.5 Material Properties

Table 5-8 shows material assignments for structural components in the truss model.

Elastic properties were assigned to the elements for Columns 143 and 144 and the spandrel. As described

in Section 3.1.2, the Hjelm material model was used for the concrete model, which allowed different yield

strengths for tension and compression. To improve convergence in the analysis, the negative slope after cracking in tension or crushing in compression was removed, and the concrete was assumed to be plasdc

after crackmg or crushing.

NISTNCSTAR 1-6C. WTC Investigation 73
Chapter 5

Creep in steel was included in the analysis; however, the creep formulation was slightly different from

Eq. (7) in Section 3.2.2. A ratio of room temperature yield strengths (i.e., 35.5 / c,,^^) was used as the

scaling factor of stress in the creep fonnulation for the truss model. NIST later changed the scaling factor

from what was used here to the ratio of room temperature ultimate strengths (i.e., 70.5 / cr^^j- ) as shown

inEq. (7).

Table 5-8. Material assignments in truss model.

Structural Component

optrCIIIcQ I ItrlQ Strength Material ID

Top chord 50ksi 21 Bottom chord 50 ksi 21

1.09 in. diameter web 36ksi 20

1.14 in. diameter web 50 ksi 21

Strap 36 ksi 1 Column 143 65 ksi 15 Column 144 65 ksi 15

Spandrel 42 ksi 11

Lightweight concrete slab 3,000 psi(fc) 83

5.4.6 Resistance Welds

Table 5-9 shows the resistance weld strength between a double angle chord and a web diagonal^ Weld

strengths shown in Table 5-9 were the sum of the capacities of two resistance welds, one on each side of

the web diagonal to each angle. Figure 5-29 compares resistance weld strength at the top or bottom

chord with the yield strength of a web diagonal at elevated temperatures. As shown in Fig. 5-29 (a), a

typical web diagonal (1.09 in. diameter) yields before the resistance weld fails. For a 1.14 in. diameter

web diagonal, the resistance weld strength is less than the web diagonal yield strength at temperatures

below 550 X, as can be seen in Fig. 5-29 (b). However, shop drawings showed additional arc welds

between the chord and 1 . 14 in. diameter bar at most locations.'*

Table 5-9. Resistance weld strength.

Chord

Size of Web Diagonal

(in.) Average Weld Strength

(kip)

Top chord 1.09 36.9 Top chord 1.14 37.7 Bottom chord 1.09 41.0

Bottom chord 1.14 40.5

Based on the test data from Laclede Steel Co.

^ Based on the test data from Laclede Steel Co.

74 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Figure 5-29. Comparison of resistance weld strength and yield strength of web member

at elevated temperatures.

5.4.7 Model Verification

Before analyzing the truss model response to elevated temperatures, the maximum vertical displacement

under dead and live loads was verified against the single truss model extracted from the ANSYS full floor

model. The maximum difference in the vertical displacement was found to be 3.5 percent. In this comparison, the effects of construction sequence were not included in either model.

5.4.8 Truss Analysis for Debris Load

The capacity of the truss model against additional debris load was determined by increasing the gravity

loads. When this analysis was performed, the truss model was still under development and somewhat

different from the model described in Section 5.4.1. Break elements were not used for studs, interior, or

exterior truss seats, nor for reinforcement at the interior end of the slab. The slab was modeled by

SHELL181 elements with elastic material properties. Boundary conditions of the slab were also slightly

different from those described in Section 5.4.3. The exterior end of the slab was tied to the spandrel

without break elements and contact elements, and the interior end of the slab was fixed in they and z

directions and against rotations about the x and z axes without break elements.

The analysis was terminated at a load factor of 3.4. Load factor is the ratio of the gravity load plus debris

weight to the gravity load. Figure 5-30 (a) shows midspan vertical displacement versus load factor. At a load factor of 2.4, Knuckles 5 to 15 failed due to horizontal shear in the truss direction. At a load factor of 2.8, Knuckle 4 failed. Figure 5-30 (b) shows the sum of the horizontal reaction forces measured at the

exterior columns, where a positive value is used when columns are pulled in by the truss. After twelve of

fifteen knuckles failed, the model lost its composite action, and the vertical displacement increased

significantly. As a result, horizontal reaction forces at the exterior columns also increased.

NISTNCSTAR 1-6C, WTC Investigation 75
Chapter 5

Exterior

1 2 3 4 5 6

\A/\/\/\

7 8 9 10 11 12 13 14 15

Interior

\

' Knucke 4 falied (only 3 knuckles are left)

Knuckles 5 to 15 failed (only 4 knuckles are intact on

the side of the exterior end)

4 6 I Displacement (in)10 12

(a) Load factor versus midspan vertical displacement

10,000 20,000 30,000 40,000 50,000 60,000

Horizontal Reaction Force (lb)

(b) Load factor versus liorizontal reaction force

Figure 5-30. Finite element analysis results from increasing gravity.

76 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.4.9 Truss Analysis for Gravity and Thermal Loads

Gravity Loading: The maximum calculated vertical deflection due to the self-weight of the structure,

which occurred when the concrete was still wet, was 1.7 in. downward. When the superimposed dead and

live loads were applied to the truss with hardened concrete slab, the maximum vertical deflection became

2.0 in., and the maximum horizontal column deflection was 0.05 in. inward. The maximum forces in the

top chord, bottom chord, web diagonal, and end diagonal strut were -25.7 kip, 41.3 kip, -6.9 kip, and

16.0 kip, respectively, which translate to average stresses of 14.8 ksi, 11.6 ksi, 6.7 ksi, and 15.7 ksi,

respectively. The yield strength of top and bottom chords and end diagonal struts was 55.3 ksi. The yield

strength of web diagonals was 38.1 ksi, except for the first compressive web diagonal at the interior end,

which had a yield strength of 55.3 ksi. Therefore, the maximum stress level was about 30 percent of yield

strength.

Gravity Plus Thermal Loading: The analysis of the truss model subjected to temperature time history was carried out statically; however, when the solution process did not converge, to overcome the

convergence problem, the problem was solved dynamically with a 5 percent Rayleigh damping. The

static analysis was then resumed when acceleration and velocity became small. The analysis proceeded in

this fashion until the temperature of the steel became 727 °C. Figure 5-31 shows the vertical displacement of the truss at 700 °C, and Fig. 5-32 shows the horizontal displacement of Column 143 at the floor level and vertical displacement of the bottom chord at midspan with temperature of steel. The

zero vertical displacement in this figure represents the initial displacement after the self-weight was

applied. A positive horizontal displacement indicates that the exterior columns were pushed out, and a negative vertical displacement indicates that the truss was deflected downward. At 445 °C, when the end

diagonal struts began to yield, the horizontal displacement at the exterior column began to decrease. At

565 °C, the truss sag became large due to the buckling of web diagonals, and the exterior columns were

pulled in.

Exterior seat \ / \ / ^/>^''' ' Interior seat

(in.) -42.11 -23.095 -13.588 -4.081 -37.357 -27.849 -18.342 -8.834 .673211

Figure 5-31. Vertical displacement at 700 °C (downward displacement is negative).

NISTNCSTAR 1-6C, WTC Investigation 77
100 200 300 400 500 600 700 800

Temperature (°C)

(a) Horizontal displacement at Column 143

0 100 200 300 400 500 600 700 800

Temperature (°C)

(b) Vertical displacement at midspan

Figure 5-32. Displacement versus temperature of steel.

NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Figure 5-33 shows selected truss members. Figure 5-34 shows the axial forces in selected truss members

Fig. 5-33. In Fig. 5-34. Py is the axial force at yield and equals the product of the net area of the member

and the yield strength which varies with temperature. Pc in Fig. 5-34 (c) is the compressive strength

calculated per the American Institute of Steel Construction's Manual of Steel construction. Load and

Resistance Factor Design (AISC 2003) for fixed end conditions. Because the top chord was tied to the concrete in the vertical direction and was restrained in the direction transverse to the truss in this model,

the failure of the top chord was by yielding, Py, rather than buckling, Pc.

Figure 5-34 (a) shows yielding of the top chords between knuckles beyond 300 °C, resulting from the

significant difference in coefficients of thermal expansion between concrete and steel. At 500 °C, the

coefficient of thermal expansion of steel was twice that of lightweight concrete. Yielding of the top chord

did not play a significant role in the truss response because of its minor contribution to the composite area of the concrete slab and steel truss. Bottom chords were still in the elastic range at the end of analysis.

Buckling of web diagonals started at approximately 565 °C. Several web diagonals were bent

significantly in the plane of the truss by the high compressive axial force (see Fig. 5-35 for the defonned

shape at the interior end).

Figure 5-36 shows knuckle forces in the longitudinal truss direction and the vertical direction. The

capacity- of a knuckle was 30 kip in shear and 15 kip in tension at room temperature. Knuckle 15 failed

due to tension around 100 °C. Knuckles 13 and 14 failed due to shear in the longitudinal truss direction at about 566 °C.

12(1 16S 199

Figure 5-33. Element numbers and locations of elements examined for axial force.

NISTNCSTAR 1-6C, WTC Investigation 79
Chapter 5

(a) Top chord

.52 "x<

(b) Bottom chord

X

<

200 400 600

Temperature (°C)

100000

80000

oj 60000 u

40000

20000

EL#168 (mid) -EL#120 (nearext) -EL#199 (near int) Py

200 400 600

Temperature ("C)

800

800

(c) Compression web

diagonal

.2

'>< <

200 400

Temperature ("C)

600 800

Figure 5-34. Axial force in truss members versus temperature of steel.

80 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

-15725 -8790 -1855 5081 12016 -12258 -5322 1613 8548 15484

Figure 5-35. Axial stress contour in the truss members at 700 °C

(tension is positive; 1.0x displacement magnification).

Figure 5-37 (a) and (b) show the horizontal reaction forces at exterior and interior truss seats and exterior

columns, respectively. At 566 °C, the interior truss seat bolts sheared off, without loss of vertical support.

At 670 °C, the gusset plate at the exterior truss seat fractured, followed by shearing of the exterior seat boh. At 730 °C, the truss walked off the exterior truss seat. At about 600 °C before failures of the gusset

plate and the exterior seat bolts, the tension between the truss and the exterior columns was about 12 kip,

which was through the gusset plate and the strap anchor. At about 700 °C after failure of the gusset plate

and the exterior truss seat bohs, the tension became about 10 kip, which was only through the strap

anchor. It was found that 10 kip tension in the strap anchor was larger than the strength at 700 °C (7.5

kip) of the weld (a size of 5/16 in. and a length of 4 in.) between the strap anchor and the top chord. The

failure of this weld was not modeled by break elements in the truss model. If the failure of this weld had

been modeled in the truss model, the walk-off could have occurred at a temperature lower than 730 °C.

Failure modes and failure sequence of the truss model subjected to "assumed temperature conditions" were as follows:

• The stud on the spandrel and studs on the strap anchor failed in shear below 275 °C.

• Knuckle 15 failed in vertical tension at around 100 °C, and Knuckles 13 and 14 failed in the

horizontal shear at 566 °C.

• Top chords yielded above 300 °C due to the difference in coefficients of thermal expansion of

steel and lightweight concrete.

• Four compression web diagonals buckled due to high axial compressive force at 565 °C.

• The interior truss seat bolts sheared off at 566 °C.

• The gusset plate fractured and the exterior truss seat bolts sheared off at around 680 °C.

• The truss walked off the exterior truss seat at 730 °C. The acmal failure modes and failure sequence in the WTC towers may have been different due to the

difference in actual and assumed temperature time histories. The truss model was simplified as described

in the next section and incorporated in the full floor model and analyzed for the actual estimates of

temperature time histories.

NISTNCSTAR 1-6C, WTC Investigation 81
Chapter 5

Exterior

1 2 3 4 5 6 7 i 9 10 11 12 13 14 15

\./\/ \/ \ / \/ \/"\./ \./ \ / \/ \/ \.7\

Interior

0)u

o

u.

30000

20000

10000

0

-10000

-20000

-30000

Knuckle 15 failed

~ capacity

—~-

-e- Knuckle 1 Knuckle 2 —^Knuckle 3 & Knuckle 13

Knuckle 14 -A- Knuckle 15

Knuckles 13 and 14 failed.

100 200 300 400 500 600 700 800

Temperature (°C)

(a) Horizontal force

g -5000

-10000

-15000

-20000

-^Knuckle 1 <»- Knuckle 2 —^Knuckle 3 & Knuckle 1

-ts^ Knuckle 14 -A- Knuckle 15

0 100 200 300 400 500 600 700 800

Temperature (°C)

(b) Vertical force

Figure 5-36. Force in the knuckles versus temperature of steel.

82 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

—o— Interior Seat —4— Exterior Seat 30000 -1 —o— Gusset Plate Interior Seat Capacity

Exterior Seat Capacity Gusset Plate Capacity

0 100 200 300 400 500 600 700 800

Temperature (°C)

(a) At truss seats

40000

Si

0 100 200 300 400 500 600 700 800

Temperature (°C)

(b) At exterior columns

Figure 5-37. Horizontal reaction forces.

NISTNCSTAR 1-6C, WTC Investigation 83
Chapter 5

5.4.10 Simplified Truss Model

The truss model was simplified for use in the full floor subsystem model. Characteristics of the truss model captured by the simplified truss model were: (1) total horizontal reaction force under the thermal

loading and (2) vertical deflection at midspan under the thermal loading. The simplified tniss model had

the following features:

• The geometry of the truss was preserved.

• A pair of primary trusses at each exterior column was combined into one truss. Cross

sections of truss members were doubled.

• The top and bottom chords and web diagonals were modeled by BEAM 188 elements. A

member between two panel points was modeled by one element only.

• Break elements modeled by ANSYS user-defined elements were used to model the following

failure modes: (a) seat bolt shear-off, (b) gusset plate fracture, (c) truss walk-off, (d) web

diagonal buckling/resistance weld failure, (e) failure of studs on the spandrel and strap

anchors, and (f) weld failure between strap anchors and top chords. User-defined break

elements will be further discussed in Section 5.5.5.

• Knuckles were not modeled by break elements. It was found that neglecting knuckle failure did not significantly change truss behavior subjected to thennal loads.

• Steel had temperature-dependent elastic and plastic material properties.

• Creep in steel was included in the simplified truss model; however, it was not included when

the simplified tmss model was incorporated in the full floor model, because of convergence

problems inherent in BEAM188 elements.

• The concrete slab was modeled by SHELL181 elements with a temperature-dependent

bilinear material model that had the same yield strength in both tension and compression.

The yield strength was set to the compressive strength.

• Construction sequence was not considered.

Figure 5-38 shows the vertical deflection at midspan and the horizontal reaction at exterior columns of

the truss model and simplified truss model subjected to the gravity load and the assumed thennal load

described in Section 5.4.4. Vertical displacement in this figure is the displacement that occurred during

thermal loading. The simplified truss model predicted the buckling of web diagonals at 530 °C, which is about 35 °C lower than the temperature at which web diagonal buckling was predicted by the truss model.

The tension at 700 °C in the simplified truss model was about 2 kip, which was less than 10 kip in the

truss model. Overall truss behaviors as predicted by the simplified truss model subjected to gravity and

the assumed thermal loading were in good agreement with the truss model.

84 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

0

-5

1-10

c

E -15 u

(A E-25

reo1 -30 >

-35

-40

!

i ; ;

s.

_

""1

Truss Model

Simplified Truss Model

, 1

.

i 1 i 0 100 200 300 400 500 600 700

Temperature (°C)

(a) Midspan vertical deflection

40

^ 20

Truss Model

1 Simplified Truss Model 1

.100 200 300 400 500 600

Temperature (°C)

700

(b) Horizontal reaction force at exterior columns

Figure 5-38. Comparison of detailed and simplified truss models.

NISTNCSTAR 1-6C, WTC Investigation 85
Chapter 5

5.5 FULL FLOOR MODEL

5.5.1 Objective

The full floor model was developed and analyzed using the ANSYS general purpose finite element

program Version 8.1. The objectives of the full floor model analysis were:

• To identify the most likely failure modes,

• To evaluate - Failure loads, - Temperatures at failure, - Time-to-failure, and - Changes in mechanical properties and geometry at failure.

• To identify the fire-induced damage to be incorporated along with impact-induced damage in

the global model

• To develop computationally efficient modeling details of the floor subsystem for

incorporation into the global model.

5.5.2 Failure Modes

Failure modes that the full floor models captured were as follows:

• Floor Sagging: Floor sagging was caused by loss of stiffness and softening of truss at high

temperature, by yielding and buckling of truss members, and by the impact damage to truss

seats. These were discussed in some detail under truss failure modes. Floor sagging resulted

in tension in the floor subsystem, tension on the connections to the exterior walls, and lateral forces (pull-in forces) on exterior columns.

• Loss of Support: Loss of a truss support was caused by reduced vertical shear resistance of

truss seats at elevated temperatures, by tension acting on truss seats caused by floor sagging,

and by aircraft impact.

5.5.3 Model Description

The base floor model developed was for Floor 96 of WTC 1 with columns extending from Floor 95 to Floor 97. The model was developed based on the converted SAP2000 model for Floor 96 of WTC 1, with the following modifications:

L Two adjacent trusses supported by the same column were combined into a single truss. The

areas of members in a truss were doubled to create a combined truss.

2. Spandrels were defined as beam sections m the SAP2000 model, and were replaced with

SHELL181 elements (eight elements between two columns and four elements along the

height). This modification eliminated the need for defining panel zone stiffness at the

interface between spandrel and exterior column.

3. Elastic column elements were changed to BEAM189 elements with user-defined composite

sections and nonlinear material properties.

86 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

4. Section offsets of exterior columns were removed, and nodes were placed at centroids of their cross sections.

5. Spandrels were tied to exterior columns by rigid beam elements as described in Section 6.4.1 of this report.

6. Core floor slab was remeshed with a more unifoiTn mesh.

7. Section offsets of core beams were removed to eliminate the end bending moment due to eccentricity. Core beams were placed at their centroids and were connected to the slab by

rigid beam elements.

8. Where there was more than one beam element representing a top chord between two adjacent

panel points, the beam elements were merged into one to prevent the top chord from buckling

upward and penetrating the slab.

9. Web diagonals were modeled by BEAM 188 elements.

10. Coincident nodes were provided for user-defined break elements.

1 1 . User-defined break elements were incorporated into the model to represent:

a. buckling of web diagonals,

b. gusset plate fracture,

c. truss seat bolt shear-off,

d. truss seat failure,

e. failure of connections between primary and bridging trusses,

f. failure of connections between primary long-span and transfer trusses,

g. failure of studs connecting the slab and the spandrel, and

h. failure of welds between strap anchors and top chords of primary trusses.

12. The ANSYS floor model translated from the SAP model had the bottom chord connection at every intersection of primary and bridging trusses. Some of the bottom chord connections

between primary and bridging trusses were removed according to the PANYNJ drawings.

The full floor model, as shown in Fig. 5-39, included the following structural members:

a. both exterior and core columns extending from one floor below to one floor above,

b. spandrels of the floor modeled,

c. floor slab,

d. floor trusses including primary and bridging trusses,

e. strap anchors,

f core beams, and

g. deck support angles.

NISTNCSTAR 1-6C, WTC Investigation 87
Chapter 5

88 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

The size of the full floor model was as follows:

• Number of elements: 46,280

• Number of nodes: 61,251

• Number of degrees of freedom: 269,926

Truss members (top and bottom chords and web diagonals) were modeled by BEAM188 elements.

Columns were modeled by BEAM189 elements. Spandrels were modeled by SHELL181 elements. The

concrete slab was modeled by SHELL 1 8 1 elements with four layers through the thickness. Each layer of

the shell element for the slab had one integration point.

The full floor model was validated against the SAP floor model by performing the two analyses described

in Section 4.2.1. To compare the full floor model with the SAP floor model, density of lightweight concrete was changed from 1 10 pcf to 100 pcf Under gravity loads, the maximmn displacement of the

full floor model was 0.722 in., which is only 0.56 percent smaller than that of the SAP floor model. The

first vibration mode of the full floor model was not the vertical deflection of the office floor, but the

lateral vibration of the bridging trusses in the short-span truss area. This was a result of removing some

of the bottom chord connections between the primary and bridging trusses. The natural frequency of the

vertical deflection mode was 4.41 Hz, which is only 2 percent higher than that of the SAP floor model.

Subsequent to initial full floor analysis with thermal loads, the members listed below were removed from

the model to enhance computational efficiency without loss of accuracy of prediction of final failure modes and failure sequence, as shown in Fig. 5^0.

• Deck support angles

• Bridging trusses outside of the two-way zones

• Spandrel studs connecting the slab and the spandrel

• Strap anchors

These elements failed in the early stage of thermal loading and caused the analysis to slow down due to large nonlinearities of the failed elements. Deck support angles and bridging trusses buckled between the

primary trusses due to thermal expansion. Many shear studs and welds between strap anchors and truss top chords failed due to lateral shear force in the direction transverse to the primary trusses caused by the

difference in thermal expansion between the floor and the exterior wall. These members were removed

from the model to enhance computational efficiency. As a result of removal of strap anchors and spandrel

studs, the only connections between the exterior wall and the floor were gusset plates and exterior truss

seats. The visco-elastic dampers that connected the truss bottom chords to the spandrels were not included in the

full floor model because dampers were expected to be soft when subjected to very slow loading rates.

The concrete slab was attached to primary trusses at knuckle locations. Break elements were not used for representing knuckle failure as the truss analysis found that web diagonal buckling rather than knuckle

failure caused floors to sag. The concrete slab and trusses were always connected in the analysis.

NISTNCSTAR 1-6C, WTC Investigation 89
Chapter 5

Figure 5-40. Full floor model after removal of deck support angles, spandrel studs,

bridging trusses outside of two-way zones, and strap anchors.

5.5.4 Material Properties

Material properties from Table 3-1 were assigned to each steel member according to the PANYNJ

drawings. The Hjelm plasticity model used for the concrete slab in the truss model can be used only with

solid elements. Since the concrete slab in the full floor model was modeled by shell elements to enhance

computational efficiency, a bilinear model with a yield point at its compressive strength was created and

assigned to the shell elements for the concrete slab. This material model required the same yield strength

values in both tension and compression, as shown in Fig. 5^1. With this material model, tensile strength

of the concrete slab was not represented accurately, and the actual floor stiffness was overestimated. In

the full floor models, bending stresses in the concrete slab that exceeded the actual tensile strength of

concrete were found in few locations. This phenomenon was typically observed when the temperature of

the top of the slab was higher than the temperature at the bottom of the slab, and the concrete slab still deflected down due to large thermal expansion of the truss. However, when the temperature is higher at the bottom, the simplified truss model with this material model showed a very similar behavior to the detailed truss model, and the key failure modes of the floors were not significantly affected.

Thermal expansion of the spandrel would cause the spandrel to buckle between columns at early stages of

thermal loading and slow down the computation, causing severe convergence problems. To enhance

computational efficiency, a bihnear material model with a yield strength lower than the elastic buckling

strength was incorporated in the spandrel to prevent its elastic buckling. Figure 5-42 shows the bilinear

model in the spandrel and the location of elements with this material model.

It was found that creep in BEAM188/189 elements would cause severe convergence problems when those

elements experience thermally-induced buckling. Therefore, creep was not included in any of the full floor analyses.

90 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

-4000 -

-5000

-0.03 -0.02 -0.01 0.00 0.01 Strain (in/in)

0.02 0.03

Figure 5-41. Bilinear material model for concrete slab in the full floor model.

16000

16000

14000

12000 a 10000 m

S 8000

6000

4000

2000

0

10

5.5.5

—T=20X —T=100X T=200*C T=300°C —T=400'C —T=500'C —T=600-C —T=700°C

0 0.005 0.01 0.015 0 02 0 025 0.03 0.035 0 04 0 045 0 05

Strain (in/in)

(a) Bilinear material model for spandrel

(only tension side is shown)

(b) Elements with the bilinear material model

(shown in pick)

Figure 5-42. Bilinear material model in the spandrel.

User-Defined Break Elements

Break elements were used to represent component failures. Break elements for the full floor model were

recreated by using user-defmed elements in ANSYS. Basically, a user-defined break element is an elastic spring. When the force or the moment in a certain direction in the element reaches its capacity, the spring

stiffnesses in all directions are reduced to the predefined post-failure stiffnesses. Initial and post-failure

stiffnesses are defined as temperature-independent properties, while the capacity can be defined as temperature-dependent properties. Different capacities can be assigned to tension and compression.

There are differences between the break elements defined by COMBIN37 elements described in Section 5.2.5 and the break elements defined by user-defined elements. First, the user-defined break

NISTNCSTAR 1-6C, WTC Investigation 91
Chapter 5

element has stiffness even after failure of the element although the post-failure stiffness is set significantly small, usually 10"' to 10'^ times the initial stiffness. Second, only one user-defmed break

element is usually required to model one failure mode, while many COMBIN37 break elements along

with elastic beam elements are required to model one failure mode.

Four different types of user-defined break elements were developed for the full floor model and the

exterior wall model, and their features are summarized in Table 5-10. Figure 5^3 shows a summary of

user-defined break element locations in the full floor model.

Table 5-10. Types of user-defined break elements.

Type Degrees

of

Freedom.

Capacities

to be

defined

Stiffness to be defined Description Usage in the

floor model

1 0? 1 lY 1 UM u vc r yv lllillal DlliillC^a lUl U-A. All \c\TC*f^ ciniH Tn (^m *=*Ti

lUlLC allU IIIUIIICIIL UY Negative FX Post-iailure stitiness lor UX components are checked Fracture of

UZ Positive FY Initial stiffness for UY with corresponding gusset plates

ROTX Negative FY Post-failure stiffness for UY capacities. Failure of

ROTY Positive FZ Initial stiffness for UZ connections

ROTZ Negative FZ Post-failure stiffness for UZ

between primary

and bridging MX Initial stiffness for ROTX

MY Post-failure stiffness for ROTX Failure of

MZ Initial stiffness for ROTY

Post-failure stiffness for ROTY

Initial stiffness for ROTZ

Pn*\t-fhilnrp stifTnpss for ROT7

connections

between long- span and transfer trusses

1 f\1 1U3 TUATV Positive F initial stillness lor ua, u y , SRSS* of three force Failure of strap

U Y Negative F

and U7 rnmnnnpnl*; i<s rHprlcpH

UZ Post-failure stiffness for UX, witH Willi IHp LllV rarvapitv ^ClL/Cl^iiy. THp 1 llw UY, and UZ

determined by the dirprtinn U11 11 \J 11 snpnfipd OL^^V^ll-lwV-i Hv\j y the user. 104 ux Positive FX Initial stiffness for UX All force components Failure of studs UY Negative FX

Positive FY

Negative FY

Positive FZ

Negative FZ

Post-failure stiffness for UX are checked with connecting the UZ Initial stiffness for UY

Post-failure stiffness for UY

Initial stiffness for UZ

Post-failure stiffness for UZ

corresponding

capacities.

spandrel and the slab

105 ux Positive F Initial stiffness for UX, UY, SRSS* of three force Buckling of web

UY Negative F and UZ components is checked diagonals

UZ Post-failure stiffness for UX, with the capacity. The Failure of

ROTX

ROTZ

UY, and UZ sign of force is resistance weld

Initial stiffness for ROTX, detennined by the between web

ROTY, and ROTZ direction specified by diagonals and

ROTZ

Post-failure stiffness for ROTX,

ROTY, and ROTZ

the user. chords

* SRS S : square-root-of-sum-of-square

92 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

o o o

(a) Web diagonal buckling or weld failure

gjisset platefracture

bolt shear-offmid walk-off

(b) Exterior seat failure

/ \ O bolt shear-off and walk-off

(c) Interior seat failure

(d) Stud failure

LH'

r I

(d) Strap anchor weld failure

\

(e) Connection failure between

primary and bridging trusses

(f) Connection failure between

long-span and transfer trusses

Figure 5-43. Summary of user-defined break element locations in the full floor model.

NISTNCSTAR 1-6C, WTC Investigation 93
Chapter 5

Table 5-1 1 gives the number of user-defined break elements in the WTC 1 Floor 96 model after the

removal of studs, strap anchors, bridging trusses, and severed members by aircraft impact, and Fig. 5-44

shows locations of the user-defmed break elements.

Table 5-11. Number of user-defined break elements in the full floor model

/Floor Q(? WTP 1 Number of break elements

Web diagonals 1.264

Studs 0

Strap anchor welds 0

Seats and gusset plates 564

Connections between primary and bridging trusses 200

Connections between long-span and transfer trusses 40

Total 2.068

ELEMENTS

SEC NUM

Diagonals: green

Seats: red Primary and bridging truss connections: blue

Long-span and transfer truss connections: pink

Figure 5-44. User-defined break element locations in the full floor model

(Floor 96, WTC 1).

AN

SEP 10 2004 09:12:21

WTCl FL96

94 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.5.6 Impact Damage

Elements corresponding to structural members that sustained severe structural damage were removed

from the model. Based on the aircraft impact analysis, NIST identified two sets of impact damage

(structural damage and insulation damage) for each of the two WTC towers. These two cases represented

a base case and a more severe case of damage estimates, and they were designated as "Case A, impact

damage condition" and "Case B, impact damage condition" for WTC 1, and "Case C, impact damage

condition" and "Case D, impact damage condition" for WTC 2. The floor model analyses were

performed by using these impact damage conditions. However, NIST later refined these impact damage

conditions, and refined cases are referred to as "Case A impact damage condition" and "Case B impact

damage condition" for WTC 1. and "Case C impact damage condition" and "Case D impact damage

condition" for WTC 2. Refined impact damage conditions were never used in the full floor model.

Figures 5-45 to 5-54 show structural impact damage conditions for different cases. Structural impact

damage to exterior coluirais did not change between Case Aj and Case Bi or between Case Ci and Case Di. Only columns that were indicated as "severed" were removed from the model, and those columns that were damaged but not severed were retained as undamaged in the analysis. Figures 5-55 through 5-60

show floor models of WTC 1 Floor 96 with and without impact damage for Case A, impact damage

condition.

Using the base floor model (WTC 1 Floor 96) as a basis, seven floor models from Floor 93 to Floor 99 of

WTC 1 were created for Case A, structural damage condition. Each model had the same geometry, but

different impact damages were incorporated. Since Case B, structural damage condition was not provided

by NIST at the time of computation, the same structural damage as Case Aj was assumed for Case Bj

condition. The WTC 2 Floor 81 model was developed by changing only column properties of the base

floor model (WTC 1 Floor 96). Floor models of other floors of WTC 2 (Floor 79, Floor 80, Floor 82, and

Floor 83) had the same geometry as the WTC 2 Floor 81 model, but had different impact damage. For

WTC 2, a total of ten models were created: five models for Case C, impact damage condition and five for Case D, impact damage condition.

NISTNCSTAR 1-6C, WTC Investigation 95
Chapter 5

(c) Floor 96; (4) Floor 97

N

Fireproofing damage

to core beams and

trusses

{§} Floor 98

Figure 5-45. Case Aj insulation damage condition for WTC 1 floor trusses and beams.

96 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Floor 94 (fe) Floor 95

(.gj Floor 98

Figure 5-46. Case Ai structural damage condition for WTC 1 floors.

NISTNCSTAR 1-6C, WTC Investigation 97
Chapter 5

Column i

s s S S s E s 1? 5 5

^_ 5 1 s 2:i_ i2H- 2

1 1 s s s*- 5 s

Floor _ —

99 Spandrel Column

98 Spandrel s S s s s** Column _n n

X_ s s 5 s n

97 Spandrel Column

n s s s s

96 Spandrel Column

95 Spandrel s s

s

Column s s s s s

94 Spandrel Column

93 Spandrel Column

92 Spandrel

(a) North face

i S 1 s s 1 S 5 1 s s s s s 5 s 1 i

° i° i i° i i

Floor 99 Spandrel Column

98 Spandrel Column

97 Spandrel Column

96 Spandrel s s s

Column s s s

95 Spandrel s s s

Column s s s

94 Spandrel s s s

Column

93 Spandrel Column

92 Spandrel

(b) South face

S: severed; D: damaged

Figure 5-47. Structural damage to exterior walls of WTC 1 for Case Aj and Case Bj impact

damage conditions.

98 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

FL100

FL99

FL98

FL97

FL96

FL95 FL94

FL93

FL92

COL501 COL601 COL701 COL801 COL901 COL1001

I D'

I D*

FL100 FL99

FL98

FL97

FL96

FL95 FL94

FL93

FL92

COL505 COL605 COL705 COL804 COL905 COL1005

FL100

FL99

FL98

FL97

FL96

FL95

FL94

FL93

FL92

COL502 COL602 COL702 COL802 COL902 COL1002 COL506 COL606 COL706 COL805 COL906 COL1006

FL100

FL99 1 1 1 1 1 1 FL98 1 1 1 1 1 1 FL97 1 1 1 1 1 1 FL96 1 1 1 1 1 1 FL95 1 1 S 1 1 1 FL94 D 1 s D 1 1 FL93 1 1 s 1 1 1 FL92 1 1 R 1 1 1

FL100

FL99

FL98

FL97

FL96

FL95

FL94

FL93

FL92

COL503 COL603 COL703 COL803 COL903 COL1003

FL100

FL99

FL9B

FL97

FL96

FL95 FL94

FL93

FL92

COL507 COL607 COL707 COL806 COL907 COL1007

COL504 COL604 COL704 COL904 COL1004

FL100

FL99 1 1 1 1 1 FL98 1 1 1 1 1 FL97 1 1 1 1 1 FL96 S A D D 1 FL95 s S D 1 1 FL94 s S 1 1 1 FL93 s 1 1 1 1 FL92 R 1 1 1 1

FL100 FL99

FL98

FL97

FL96 FL95

FL94

FL93

FL92

COL508 COL608 COL708 COL807 COL908 COL1008

I D*

I D*

1: intact A: alignment affected

D: damaged (plastic strain present) S: severed

R: rotated *: column connections show plastic strains

Figure 5-48. Structural damage to core columns of WTC 1 for Case Aj Impact damage

condition.

NISTNCSTAR 1-6C. WTC Investigation 99
Chapter 5

nil

(a) Floor 79

4.

iUliii!

. I.,

1

(c) Floor 81

.JXXXXZJ

^A. I

<

TT

(b) Floor 80

(d) Floor 82

n

I

Fireproofing damage

to core beams and

trusses

(e) Floor 83

Figure 5-49. Case Cj insulation damage condition for WTC 2 floor trusses and beams.

100 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(c) Floor 81 (d) Floor 82

(e) Floor 83

Figure 5-50. Case Ci structural damage condition for WTC 2 floors.

NISTNCSTAR 1-6C, WTC Investigation 101
Chapter 5

(c) Floors! (d) Floor 32

1

Fireproofing damage

to core beams and

trusses

(e) Floor 83

Figure 5-51. Case D; insulation damage condition for WTC 2 floor trusses and beams.

102 NISTNCSTAR 1-6C, WTC Investigation
Full hloor Subsystem

(a) Floor 79

(c) Floor 81

'7T7TT - • •

' Tfttt" ,

(b) Floor 80

(d) Floor 82

N

Structural damage to concrete slab, core beams, and trusses

(e) Floor 83

Figure 5-52. Case Dj structural damage condition for WTC 2 floors.

NISTNCSTAR 1-6C, WTC Investigation 103
Chapter 5

Column 1 (5 5 o o o s s o o

Floor 85 Spandrel Column

84 Spandrel Column

83 Spandrel Column

82 Spandrel Column

81 Spandrel Column D S

80 Spandrel Column

79 Spandrel Column

78Spandrel Column

77 Spandrel

(a) North face

Column 443 5/ Floor 85 Spandrel Column

84 Spandrel Column s s

83 Spandrel s s s s s d d Column s s s s s s s s

82 Spandrel D D D D D s s s s s s s

Column s s s s s s s s s s s s

81 Spandrel D s s s s s s s s Column s s s s s s s s s

80 Spandrel D D D D S s s s D D D s s s Column s s s s s S s S S s s s s 5 s

79 Spandrel s s s s S s s D D D Column s 8 S s s s D s s s D D

78Spandrel Column

77 Spandrel

(b) South face

S: severed; D: damaged

Figure 5-53. Structural damage to exterior walls of WTC 2 for Case Cj and Case D; impact

damage conditions.

FL85

FL84

FL83

FL82

FL81 FL80 FL79

FL78

FL77

COL1001 COL1002 COL1003 COL1004 COL1005 COL10D6 COL1007 COL1008

FL85

FL84

FL83

FL82

FL81 FL80

FL79

FL78

FL77

COL701 COL702 COL703 COL704 COL706 COL706 COL707 COL708

FL85

FL84

FL83

FL82

FL81 FL80

FL79

FL78

FL77

COL901 COL902 COL903 COL904 COL905 COL906 COL907 COL90B

FLeS

FL84

FLBS FL82

FL81 FL80

FL79

FL78

FL77

COL601 COL602 COL603 COL604 COL605 COL606 COL607 COL608

FL85

FL84

FL83

FL82

FL81 FL80

FL79

FL78

FL77

COL801 COL802 COL803 COL804 COL805 COL806 COL807

FL85

FL84

FL83

FL82

FL81 FL80

FL79

FL7e

FL77

COL501 COL502 COL503 COLS04 COL505 COL506 COL507 COL508

1: Intact A: Alignment affected

D: Damaged (plastic strain present) S: Severed

R: Rotated

Figure 5-54. Structural damage to core columns of WTC 2 for Case Cj impact damage

condition.

104 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Model without damage (b) Model with damage

Figure 5-55. Case Aj structural impact damage condition for exterior columns of the

north face in the WTC 1 Floor 96 model.

(a) Model without damage (b) Model with damage

Figure 5-56. Case Ai structural impact damage condition for exterior columns of the

south face in the WTC 1 Floor 96 model.

NISTNCSTAR 1-6C, WTC Investigation 105
Chapter 5

106 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

North

AN

SEP 2 20114 TYPE HUM North

AN

(a) Model without damage (b) Model with damage

Figure 5-59. Case Aj structural impact damage condition for core beams in the WTC 1 Floor 96 model.

AN

^1^

North

(a) Model without damage

ELEMENTS

TVPE KUM AN

<<>>4,

North

(b) Model with damage

Figure 5-60. Case Ai structural impact damage condition for core columns in the WTC 1 Floor 96 model.

5.5.7 Gravity and Thermal Loads

The full floor model with impact damage included was first analyzed for gravity dead and live loads, and

then temperature time histories representative of the WTC fire conditions were applied to analyze its path-dependent nonlinear structural response. Gravity dead and live loads consisted of self-weight, 8 psf

superimposed dead load, and 25 percent of design live loads. Design live loads varied from 55 psf to 85 psf as shown in Fig. 5-61. Vertical loads were not applied to the top of columns.

NIST derived the temperatures of structural components from fire models of the WTC towers and the

thermal insulation damage conditions. Temperature cases provided by NIST were "Case A, temperature

condition" and "Case Bi temperature condition" for WTC L, and "Case C, temperature condition" and

NISTNCSTAR 1-6C. WTC Investigation 107
Chapter 5

"Case Di temperature condition" for WTC 2. The floor model analyses were performed by using these

temperature conditions. However, NIST later refined these temperature conditions based on the refined

impact damage conditions, and the refined cases were "Case A temperature condition" and "Case B

temperature condition" for WTC 1, and "Case C temperature condition" and "Case D temperature

condition" for WTC 2. For the WTC 1 Floor 97 full floor model only. Case A temperature condition was

also used. Since the resuhs from the WTC 1 Floor 97 analysis for Case A temperature condition was very

similar to those for Case A„ it was concluded that the refined temperature cases would not change the

floor behavior significantly. Therefore, other floors were not run with the refined temperature conditions.

Temperature data sets were provided at 1 0 min intervals up to 1 00 min for WTC 1 and up to 60 min for WTC 2 for each temperature condition. In the first step of thermal loading, temperatures were linearly

ramped from room temperature (20 °C) to the temperatures specified at 10 min. After the first step,

temperatures were varied linearly to the next specified temperatures. Figures 5-62 to 5-65 show Case Ai

and Case Bj temperature conditions for Floor 96 of WTC 1, and Figs. 5-66 to 5-69 show Case C, and

Case D, temperature conditions for Floor 82 of WTC 2. These figures show that high temperature occurs

in trusses where there is insulation damage. Severed members are also shown in these figures; however,

severed members were not included in the analysis. Table 5-12 shows a list of full floor analyses

performed in this study.

55 psf 70 psf 55 psf I

Note: 25 percent of the design live load was applied in the analysis.

Figure 5-61. Design live load distribution in Floor 96 of WTC 1.

Temperatures were assigned at node locations for beam elements. Only columns had temperature

gradients across their cross sections; trusses and spandrels had uniform temperatures within their cross

sections. Slab temperatures were assigned at node locations. Shell elements for the slab had four layers

through thickness, and there were five points across the thickness to define the temperature distribution

through the thickness at each node location.

Temperature cases were formerly called by different names. Case D, and Case C, conditions were called "baseline case", and Case Bj and Case D, conditions were called "maximum damage case". Case A and Case C conditions were called "best estimate case" or "realistic case", and Case B and Case D conditions were called "upper bound case" or "severe case". These

former temperature case names may appear on graphics produced in ANSYS.

108 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

TiXE=3ATU5SE

South

.urn

AN

(a) Top view at 10 min (b) Top view without concrete slab at 10 min

AN

South ^p^P' West

I

AN

South .,ih ''^^'^iilli!! W(^st

Last

(c) I op View at bU mm (q; I op View wiinoui concrete siao ai du mm

AN

South

AN

temperature; TMIN-26.655

TKAJ(-77i South

(e) I op view at lUU mm (T) I op view without concrete slab at lUU mm

Figure 5-62. Case Aj temperature condition for Floor 96 of WTC 1 at 10 min, 50 min, and

100 min.

NISTNCSTAR 1-6C, WTC Investigation 109
Chapter 5

TEMFEPATURE^ AN

TMiN-;n Last AN

South North South North

1 '

r

I

iBIHi^SSiSfflii^i^i,-, ___-,..„ — „—— — l.L?2BWWt \ '

(a) Top surface at 10 min (b) Bottom surface at 10 min

ELEI'ENTE TEMPERATURE?

TMIN-:;0 West

AN AN

TKAX-SIO.IC- Ti-iAx-?;o.ie:-

South

......

North South

r

North

mmm:i..iMw.^ii.ii)i..^.:',i.,.^ „ - —, , , u.jwiw, v /

i r-cc "OC yfC : ( ( 3c[' 9c;(.

(c) Top surface at 50 min (d) Bottom surface at 50 min

AN

(e) Top surface at 100 min

South

East

AN

North

(f) Bottom surface at 100 min

Figure 5-63. Case Ai temperature distribution in the slab for Floor 96 of WTC 1 at 10 min,

50 min, and 100 min.

110 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

AN

(a) Top view at 10 min (b) Top view without concrete slab at 10 min

AN

(c) Top view at 50 min

AN

,1 'Hl'l', South West

' North

800 9^0

(d) Top view witiiout concrete slab at 50 min

East ^^^tf^^^*^" A^^'-^^

800 950

(e) Top view at 100 min (f) Top view without concrete slab at 100 min

Figure 5-64. Case Bj temperature condition for Floor 96 of WTC 1 at 10 min, 50 min, and

100 min.

NISTNCSTAR 1-6C, WTC Investigation 111
Chapter 5

TEWrERATIIRES West

AN ELEi-lENTS East

AN

South

f

, , ||

North

"—I'li'ii I'll If ii ' III'

1

(a) Top surface at 10 min (b) Bottom surface at 10 min

West

AN

South North

(c) Top surface at 50 min

AN

South North

f

MiuiiiLm . '.%;rmm\^i

1 ; ''.ci 7cc 9CC

(d) Bottom surface at 50 min

AN

(e) Top surface at 100 min

TEMPERATURES

South

East

AN

North

(°C)

(f) Bottom surface at 100 min

Figure 5-65. Case Bj temperature distribution in the slab for Floor 96 of WTC 1 at 10 min,

50 min, and 100 min.

12 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Top view at 10 min (b) Top view without concrete slab at 10 min

AN

(c) Top view at 30 min (d) Top view without concrete slab at 30 min

AN

East ,

, South

(e) Top view at 60 min

AN

(f) Top view without concrete slab at 60 min

Figure 5-66. Case Cj temperature condition for Floor 82 of WTC 2 at 10 min, 30 min, and

60 min.

NISTNCSTAR 1-6C, WTC Investigation 113
Chapter 5

South

AN

East West

(a) Top surface at 10 min (b) Bottom surface at 10 min

AN

South

East West

200 gor

(c) Top surface at 30 min (d) Bottom surface at 30 min

South

AN

(e) Top surface at 60 min

IA>t=939.flSl

East

North

1

AN

West

8GC 95Q

(f) Bottom surface at 60 min

Figure 5-67. Case Cj temperature distribution in the slab for Floor 82 of WTC 2 at 10 min,

30 min, and 60 min.

114 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

East

AN

2«(°C)

(a) Top view at 10 min

AN

TEMFEKATUREE

TMIN--10.5;:

Fnvt

4-, So.//,

North

1

(b) Top view without concrete slab at 10 min

(c) Top view at 30 min (d) Top view without concrete slab at 30 min

AN

(e) Top view at 60 min

AN

(°C)

800 950

(f) Top view without concrete slab at 60 min

Figure 5-68. Case Dj temperature condition for Floor 82 of WTC 2 at 10 min, 30 min, and

60 min.

NISTNCSTAR 1-6C, WTC Investigation 115
Chapter 5

(a) Top surface at 10 min (b) Bottom surface at 10 min

Smith

East

AN

West

TOT yoc;

(c) Top surface at 30 min

North

AN

ICC 300

(d) Bottom surface at 30 min

TEMPERATURE? South

AN

(e) Top surface at 60 min

TEHPERATUREE

TMAX-90e.2ei

East

Nofth

AN

West

i{°C)

(f) Bottom surface at 60 min

Figure 5-69. Case Dj temperature distribution in the slab for Floor 82 of WTC 2 at 10 min,

30 min, and 60 min.

116 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Table 5-12. List of 1 ull floor mode analyses performed.

Analysis # Tower Floor Impact Damage Temperature

1 WTC 1 Floor 93 Case A, Case A,

WTC 1 Floor 94 Case A, Case A,

3 WTC 1 Floor 95 Case Aj Case A,

4 WTC 1 Floor 96 Case Aj Case A,

5 WTC 1 Floor 97 Case A, Case A,

6 WTC 1 Floor 98 Case A, Case A,

7 WTC 1 Floor 99 Case A, Case A,

8 WTC 1 Floor 93 Case A, Case B,

9 WTC 1 Floor 94 Case A, Case B,

10 WTC 1 Floor 95 Case Aj Case B,

1

WTC 1 Floor 96 Case A, Case Bj

12 WTC 1 Floor 97 Case Aj Case Bj

13 WTC 1 Floor 98 Case A, Case B,

14 WTC 1 Floor 99 Case A, Case B,

15 WTC 2 Floor 79 Case C, Case C,

16 WTC 2 Floor 80 Case Cj Case C,

17 WTC 2 Floor 81 Case C, Case C|

18 WTC 2 Floor 82 Case C, Case C,

19 WTC 2 Floor 83 Case Cj Case C, 20 WTC 2 Floor 79 Case D| Case D,

21 WTC 2 Floor 80 Case D, Case Dj

-)-) WTC 2 Floor 81 Case D, Case Dj

23 WTC 2 Floor 82 Case D| Case Dj

24 WTC 2 Floor 83 Case D, Case D|

25 WTC 1 Floor 97 Case A, Case A

5.5.8 Boundary Conditions

Both core and exterior columns were supported in the vertical direction at the bottom. When the column

below the floor was severed by aircraft impact, the top of the column above the floor was supported in the

vertical direction. Core columns were free in the horizontal directions and fixed against all rotations at the top and bottom ends. Exterior columns were fixed for translation perpendicular to the face of the

building and against rotation about the axis parallel to the face of the building at the top and bottom.

They were also fixed in torsion at the top and bottom. A quantitative study of the effect of column

boundary conditions is discussed in Section 5.5.16.

5.5.9 Results from WTC 1 Floor 96 under Case Ai Temperature Condition

Vertical Displacement: Figure 5-70 shows the vertical displacements of Floor 96 for Case Aj temperature

condition at 10 min, 50 min, and lOOmin. The maximum displacement of 23 in. occurred at 10 min in the

north office area. Then, the vertical displacement decreased in the north office area as the fire moved

away from the area. The floor in the south office area started to deflect upward at 20 min, and part of the

NISTNCSTAR 1-6C, WTC Investigation 117
Chapter 5

south office area deflected upward at 70 min. Most short-span trusses also deflected upward. In the early

stage of Case Aj temperature condition, the temperature in the slab was much higher than that in the

trusses in the south office area as can be seen in Figs. 5-62 and 5-63 because the insulation was intact on

the trusses in the south office area. Although the coefficient of thermal expansion (CTE) of steel is larger

than that of concrete (50 percent larger at room temperature; the difference increases as temperature

becomes higher), when the difference in temperature between the slab and the trusses becomes large

enough to cause the thennal expansion of the slab to be greater than that of trusses, the floor deflects

upward. At 80 min, several trusses in the south office area started to deflect downward, which was

caused by the buckhng of the floor due to compression in the east-west direction. At 100 min, the

maximum downward displacement of the floor in the north area was 12.8 in., reflecting the cooling that took place, and the maximum vertical displacements in the south office area were 4.8 in. upward and 6.4

in. downward.

Behavior ofExterior Columns on North and South Faces: Figure 5-71 shows the displacements of

exterior columns normal to the face of the building at 10 min, 50 min, and 100 min. The maximum

outward displacements were 5.8 in. and 3.7 in. for the north and south faces, which occurred at 70 min

and 90 min after the impact, respectively. Exterior columns were pushed out by the floor throughout the

duration of the thermal loading. Figure 5-72 shows the horizontal reaction at each column on the north

and south faces. Since even number columns were not connected to trusses and spandrel studs and strap

anchors were removed, reaction forces at even number columns were small. In the figure, the reaction

force is positive when the floor pulls the exterior column in. Since exterior columns were always pushed

out by the floor during the analysis, reaction forces were always negative. Sagged floors did not pull in the exterior wall in this analysis.

Break Elements: Figure 5-73 shows the locations of user-defined break elements that failed by 1 00 min.

Table 5-13 gives the number of failed user-defined break elements. Many web diagonals buckled in the

northeast half of the office area where the insulation on the trusses was removed by the aircraft impact. In

the south office area, there were only a few web diagonals that buckled because the insulation on the

trusses was not damaged by the aircraft impact for Case Aj impact damage condition. By 100 min, about

70 percent of all the primary and bridging tmss connections in the two-way zones and the long-span and

transfer truss connections had failed at their top chord connections, but remained comiected at their

bottom chord cormections at most of these locations. None of the truss seats failed during the analysis;

therefore, all trusses were still connected to the exterior wall.

Effect of Vertical Loads to Columns: Another analysis was made with vertical loads applied to columns

that were obtained from the SAP2000 floor model without impact damage. Core columns yielded when

their temperatures exceeded 600 °C. However, the floor behavior did not change significantly from the

analysis without the vertical loads on columns.

118 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Figure 5-70. Vertical displacement of WTC 1 Floor 96 for Case Ai temperature condition

at 10 min, 50 min, and 100 min (downward displacement is negative; 5x displacement

magnification).

NIST NCSTAR 1-6C, WTC Investigation 1 1
Chapter 5

KODAL SCL'.'l STEP-2 AN

1 1 >u

East

!

I

(

I I I I I M

West

OiitM'ard displacement is in positive

6(in.

(a) North face at 10 min

NODAL SOLL'TJOl AN

East

1

1 1 i

1

1

!

I M {

i

1

1

i !

I

i

I i I

i i I ! 1 1 i I I ! i M I I I i ii i I West

Outw ard displacement is in negative

r(in.)

(b) South face at 10 min

I'.jDAL SOLI'TION

DMX -5.371

SMN — .048fl65 SMX -S.jJS

1 I M I I M M East

AN

!|IH!|

i 1 1 i

'III! 1 1 1

1

1

1

' I ! I

1 1 1 1 M 1 1 i li West

Outivard displacement is in positive

(in.

(c) North face at 50 min

AN

!|!nH!l'|'il|H!)|'ii!l'l'

I i

i 1 1 n li 1 1 ! i h 1 1 1 ii I i 1 1 1

East

1 i M i

I

I i

! i

I M

I i I h h i

1 1 1 M West

Outward displacement is in negative

i(in.)

-1 .47f - .86^606

(d) South face at 50 min

AN

||

I

!

I

! mil

ilililill i East West

Outward displacement is in positive

(in.

Bise Lir,^- Terr.cersture at 60CP

(e) North face at 1UU mm

AN

M !

i III

lli I I East West

Outward displacement is in negative

.(in.)

;TCi f:;!C - b^s

(t) bouth race at lUU min

Figure 5-71 . Horizontal displacement of exterior columns of Floor 96 of WTC 1 for

Case Aj temperature condition at 10 min, 50 min, and 100 min.

120 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

100

50

-200

—600 sec —1 ,200 sec —1,800 sec —3, 000 sec —4,200 sec —6.000 sec

160 150 140 130 120 Column ID

(a) North face

110 100

100 T

50 -

"a. 12

Ion 0

React -50

c

o

Kl -100 -

Hori;

-150

-200

—600 sec —1 ,800 sec

•—4,200 sec

-1,200 sec

- 3,000 sec

-6,000 sec

360 350 340 330 320 Column ID

(b) South face

310 300

Figure 5-72. Horizontal reaction force per column of WTC 1 Floor 96 for Case Aj

temperature condition.

ELEMENTS

SEC NUH

V.TCl FL96 - Base Line Temoerature at 6000 sec

AN

SEP 10 2004 09:19:30

Diagonals: green

Seats: red Primary and bridging truss connections: blue

Long-span and transfer truss connections: pink

Figure 5-73. User-defined break elements that failed by 100 min in the model of WTC 1 Floor 96 for Case Aj temperature condition.

NISTNCSTAR 1-6C, WTC Investigation 121
Chapter 5

Table 5-13. Number of failed user-defined break elements in the model of WTC 1 Floor 96 for Case Aj temperature condition.

Number of Break Elements

Web diagonals 56

Seats and gusset plates 0

Connections between primary and bridging trusses 75

Connections between long-span and transfer trusses 14

Total 145

5.5.10 Results from Other WTC 1 Floors under Case Ai Temperature Condition

Table 5-14 summarizes the maximum vertical displacements of WTC 1 floors for Case Aj temperature

condition. Figures 5-74 to 5-79 show vertical displacements of WTC 1 floors under Case Ai temperature

condition when each floor experienced the maximum displacement. Floor 95 to Floor 98 showed a significant vertical displacement in the north office area near the impact damage where truss insulation was damaged. The maximum vertical displacement of all floors was 32 in. at Floor 97 at 60 min. The

vertical displacement in the south office area was found to be insignificant on all the floors throughout the

thermal loading. Note that no truss insulation was damaged in the south office area of WTC 1 floors for Case A, temperature condition.

Figure 5-80 (a) shows the average horizontal displacement due to thermal expansion of floors at 100 min

on each face, while Fig. 5-80 (b) shows the average total thermal expansion of floors at 100 min in two

orthogonal directions. The total floor expansion ranged from 4 in. to 8 in. Figure 5-81 shows horizontal

reaction force at individual columns of the north and south faces of Floor 97. In this figure, the reaction is positive when the column is pulled inward by the floor. As can be seen in the figure, abnost all the

columns were pushed outward by the floor. This was also the case for other floors. Many web diagonals of Floor 95 to Floor 98 buckled in the hot zones of the north office area where the

truss insulation was damaged. Although gusset plates at the exterior truss seats fractured at several

locations, a complete disconnection of the floor from the exterior wall was not found in any floor.

Results from WTC 1 Floor 97 under Case A temperature condition were found to be very close to those

from WTC 1 Floor 97 under Case Aj temperature condition, and, hence, will not be presented separately

in this report.

122 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

Table 5-14. Maximum vertical displacement of WTC 1 floors for

Floor Max. Displacement

(in \ (in.)

Time at the Maximum

(min)

J

>

.HA jU'X(^

1 no

95 30.9 10 96 23.3 10 97 31.5 60

98 26.4 30

99 7.0 50

vrc: r^ij3 - b^s^

(a) Entire model

AN

SUE -22 TIME-ieoo

U2 (AVGl RStS-0

DMX -5.5€7 SMN —5.57:

SMX -3.54

AN

(in.)

(b) Top view without slab

Figure 5-74. Vertical displacement of WTC 1 Floor 93 for Case Aj temperature condition

at 30 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6C, WTC Investigation 123
Chapter 5

(a) Entire model (b) Top view without slab

Figure 5-75. Vertical displacement of WTC 1 Floor 94 for Case Aj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure 5-76. Vertical displacement of WTC 1 Floor 95 for Case Aj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

124 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Entire model

NODfyL SUJ-UTIOI STEP-7

SUB -9 TIME-ieOO

-27.334

& Line Tempe:

-i$.ie7

le at 360t

AN

N

(in.

(b) Top view without slab

Figure 5-77. Vertical displacement of WTC 1 Floor 97 for Case Aj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure 5-78. Vertical displacement of WTC 1 Floor 98 for Case Aj temperature condition

at 30 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6C, WTC Investigation 125
Chapter 5

(a) Entire model (b) Top view without slab

Figure 5-79. Vertical displacement of WTC 1 Floor 99 for Case Aj temperature condition

at 50 min (downward displacement is negative; 5x displacement magnification).

2 3 4 5 Slab Expansion (in)

(a) Average displacement of each face

23456789 Total Slab Expansion (in)

(b) Average slab expansion in each direction

Figure 5-80. Average thermal expansion of WTC 1 floors at 100 min for Case Aj

temperature condition.

126 NISTNCSTAR 1-6C. WTC Investigation
Full Floor Subsystem

100 100

-200 140 130 120 Column ID

(a) North face

360 350 340 330 320 Column ID

(b) South face

310 300

Figure 5-81. Horizontal reaction force per column of WTC 1 Floor 97 for Case Aj

temperature condition.

5.5.11 Results from WTC 1 Floors under Case Bj Temperature Condition

Table 5-15 summarizes the maximum vertical displacement of WTC 1 floors for Case B, temperature

condition, and Figs. 5-82 to 5-88 show the vertical displacements of WTC 1 floors when each floor

experienced the maximum displacement. The maximum vertical displacements of Floor 95 to Floor 98

increased due to higher temperatures when compared to those for Case Aj temperature condition,

especially in the south office area. The increase in temperatures in the south office area was a result of

impact damage to insulation on floor trusses in the area. The maximum vertical displacement among all floors was 49 in. in the south office area of Floor 98, as shown in Fig. 5-87. The large displacement on

the south side of Floor 98 was caused by the exterior truss seat failures between Column 329 and Column

343 that started between 80 min and 90 min. Exterior truss seats at Column 337 to Column 347 of Floor

97 also failed, which caused 37 in. of vertical displacement in the south office area. These exterior truss seats failed by losing vertical shear strength due to extreme temperatures of greater than 800 °C. Exterior

seat failures of Floor 97 and Floor 98 are shown in Fig. 5-89.

Figure 5-90 (a) shows the average horizontal displacement due to thermal expansion of floors at 100 min

on each face, while Fig. 5-90 (b) shows the average total thermal expansion of floors at 100 min in two

orthogonal directions. The total floor expansion ranged from 5 in. to 8.5 in. Figures 5-91 and 5-92 show

the horizontal reaction force at individual columns of north and south faces of Floor 96 and Floor 98. In these figures, the reaction is positive when the column is pulled inward by the floor. Although almost all the columns were pushed outward by the floor, it was found that large vertical displacement of the floor would reduce the compression between the floor and the exterior wall. By comparing Fig. 5-72 (b) and

Fig. 5-91 (b), one can see that the compressive forces at Columns 323 to 337 on the south face decreased

significantly for Case B, temperature condition. It should be also noted in Fig. 5-92 (b) that the

compressive forces became almost zero at columns where the floor was discormected.

Many web diagonals of Floor 95 to Floor 98 buckled in the hot zones of the north and south office areas where the truss insulation was damaged. In addition to exterior seat failures (see Fig. 5-89) that occurred on the south face, gusset plates and seat bolts at the exterior truss seats failed at several locations on the

north face; however, failures of gusset plates and seat bolts did not cause complete disconnection of the

floor from the exterior wall.

NiSTNCSTAR 1-6C, WTC Investigation 127
Chapter 5

Table 5-15. Maximum vertical displacement of WTC 1 floors

for Case Bj temperature condition.

Floor Max. Displacement

(in.)

Time at the Maximum

(min)

93 -5.8 100

94 12.7 100

95 29.2 10 96 28.6 10 97 37.4 100

98 49.0 100

99 6.8 100

Note: Negative value represents upward displacement in this table.

(a) Entire model (b) Top view witliout slab

Figure 5-82. Vertical displacement of WTC 1 Floor 93 for Case Bj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

128 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Entire model

s(in.)

(b) Top view without slab

Figure 5-83. Vertical displacement of WTC 1 Floor 94 for Case Bj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

-21.. 221 -iJ.;5i# -i.i^e e.yct

wrCl FL95 - WaXlfr.jiT &air.ag» Cas<> T*fBp€-fature at 60C s»c

:~4—

-1

'2

:— — —I. Fr

j

|!

AN S

A-

-2&.^91 -IT.aS^ -lO.^iTT -^.yll -^.530 vrc" Fl^'. - Haximj;^ Dumoge Car.e Temperaturg at 6C0 sec

(a) Entire model (b) Top view without slab

Figure 5-84. Vertical displacement of WTC 1 Floor 95 for Case Bj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6C, WTC Investigation 129
Chapter 5

(a) Entire model (b) Top view without slab

Figure 5-85. Vertical displacement of WTC 1 Floor 96 for Case Bj temperature condition

at 10 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure 5-86, Vertical displacement of WTC 1 Floor 97 for Case Bi temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

130 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Entire model (b) Top view without slab

Figure 5-87. Vertical displacement of WTC 1 Floor 98 for Case Bj temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

-6.T62 -4.392 .3fi"?i25 -5.517 -S.ZC -.837*4 : .531 WTC. n.99 - HaxiToit Oaaag** Cas^ Te^perat-jr^ at 6CCC sec

[ : I [zr;— ...

1 f

p::::i::i7:t:::i

i

i

: [..4—i........

t • '

i " M":"h":'

AN S

-e .7C3 -'1 . -^LL -5.535 -3.iae -.86iei

vr-c. ":&g - Kaxini'jm Pamoge Cos-^ Temoeratijie at 60CC sec

(a) Entire model (b) Top view without slab

Figure 5-88. Vertical displacement of WTC 1 Floor 99 for Case Bi temperature condition

at 100 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6C, WTC Investigation 131
Chapter 5

(a) Floor 97 (b) Floor 98

Figure 5-89. Loss of vertical supports in Floor 97 and Floor 98 of WTC 1 for Case Bi

temperature condition at 100 min (1x displacement magnification).

100 100

—X— West

92 1

1 0 1 2 3 4 5 6 Slab Expansion (in)

(a) Average displacement of each face

92 ': ! \ 1 1 234567891

Total Slab Expansion (in)

(b) Average slab expansion in each direction

Figure 5-90. Thermal expansion of WTC 1 floors at 100 min for Case Bj conditions.

132 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

100

50 - —600 sec —1,800 sec —4,200 sec

140 130 120 Column ID

(a) North face

- 1 ,200 sec

3,000 sec

-6,000 sec

100

100

50 -

-100

-150

-200360

—600 sec — 1,200 sec —1,800 sec —3,000 sec

4, 200 sec —6,000 sec

(b) South face

Figure 5-91. Horizontal reaction force per column of WTC 1 Floor 96 for Case Bj

temperature condition.

350 340 330 320 310 300 Column ID

100 100

-200 -200 160 150 140 130 120 Column ID

(a) North face

110 100 360 350 340 330 320 Column ID

(b) South face

310 300

Figure 5-92. Horizontal reaction force per column of WTC 1 Floor 98 for Case Bj

temperature condition.

5.5.12 Results from WTC 2 Floor 82 under Case Cj Temperature Condition

Vertical Displacement: Figure 5-93 shows the vertical displacements of WTC 2 Floor 82 at 10 min,

30 min, and 60 min. The maximum vertical displacement after the impact was 5 in. in the southeast area near the impact damage. At 50 min, trusses at Column 301 to Column 317 near the northeast comer lost their vertical support at the exterior truss seats, and the vertical displacement in this area increased

significantly. A maximum displacement of 45 in. occurred at 60 min in the northeast comer area. The

west office area did not show significant vertical displacement because the insulation on tmsses was

intact.

Behavior ofExterior Columns on East and West Faces: Figure 5-94 shows the horizontal

displacements of the exterior columns normal to the face of the building at 10 min, 30 min, and 60 min.

NISTNCSTAR 1-6C. WTC Investigation 133
Chapter 5

The maximum outward displacements were 3.8 in. and 1.6 in. for the east and west faces, respectively, at 60 min after the impact. In general, the exterior columns had outward displacement except for the north

side of the east face where there was an inward displacement of about 0.8 in. at 10 min. This inward

displacement was caused by the temperature gradient in the cross section of the exterior columns. Figure

5-95 shows the horizontal reaction at each column on the north and south faces. Since even number

columns were not connected to trusses and spandrel studs and strap anchors were removed, reaction

forces at even number columns were small. In the figure, the reaction force is positive when the floor

pulls the exterior column in. It was found that both faces experienced compression from the floor

tliroughout the thermal loading; however, several columns of the east face near the northeast comer lost

lateral support from the floor, and the reaction forces at these columns became very small.

Break Elements: Figure 5-96 shows the locations of user-defined break elements that failed by 60 min.

Table 5-16 summarizes the number of failed user-defined break elements during the analysis. A

significant number of web diagonals buckled in the east office area where insulation on the trusses was

damaged by the aircraft impact. By 60 min, about 70 percent of all the primary and bridging truss connections in the two-way zones and the long-span and transfer truss connections failed at their top

chord connections; however, at the majority of these locations, they were still connected at their bottom

chord connections. By the end of the thermal loading, gusset plates fractured at 19 exterior truss seats, bohs sheared off at 1 8 exterior truss seats and 1 interior truss seat, and 8 exterior truss seats failed in vertical shear. Figure 5-97 shows the deformed shape of the floor trusses after loss of their vertical

support at the exterior truss seats.

134 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Entire model at 10 min

.\—

: .0

i I....IT. -

AN

Tfnrr

.(in.)

-19.991 -i';.CjS eline Teir.perature at 6Cf

(b) Top view without concrete slab at 10 min

*(in.)

AN

(c) Entire model at 30 min (d) Top view without concrete slab at 30 min

n»e-;-i«

K7C; -I'r; - Baseline T*'rc»rature at 36CC- -.^^

(e) Entire model at 60 min

STSP-"

SWB -5": TJME-5e00

i

i

i

- -]-

1

!

1

r TIT'

1

AN

V

(in.)

ri.82 - Biseline Temoerature at 3C0C sec

(t) I op View without concrete slab at bU mm

Figure 5-93. Vertical displacement of WTC 2 Floor 82 for Case Cj temperature condition

at 10 min, 30 min, and 60 min (downward displacement is negative; 5x displacement

magnification).

NISTNCSTAR 1-6C, WTC Investigation 135
Chapter 5

AN

North South

Outward displacement is iii positive

(in.)

(a) West face at 10 min

AN

North

h!:iiil!ll|HI|iiy!i|4i I 1

i hi

South

Outward displacement is in negative

(in.)

(b) East face at 10 min

I I North

AN

11 1 i South

OutVi'ard displacement is in positive

.(in.)

(c) West face at '6^ mm

AN

i

! i i H i M n i M M : r 1 1

1

1 n i iI 'Ml North South

OutM'ard displacement is in negative

Fl.ei - EJ5se-_

(d) bast face at 30 mm

DMX -2.818

SMN — .013086 SW. -1.641

I I North

AN

!

I M I

I M M '|i|'M

South

i Outward displacement is in positive

r(in.

ratijre at 36C0

(e) West face at bO mm

North

AN

iiihlMlilil South

Oiihvard displacement is in negative

(in.)

Temp-^raturp at 3GGL

(t) Last face at bO mm

Figure 5-94. Horizontal displacement of exterior columns of WTC 2 Floor 82

for Case Cj temperature condition at 10 min, 30 min, and 60 min.

136 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

100

50

-200

—600 sec

, —1 .800 sec —3, 000 sec

—1.200 sec — 2,400 sec —3.600 sec

160 150 140 130 120 Column ID

(a) West face

110 100

-200360 350 340 330 320 Column ID

(b) East face

310 300

Figure 5-95. Total horizontal reaction at exterior columns on east and west faces of

WTC 2 Floor 82 for Case C, conditions.

ELEMENTS AN

SEC MUM OCT 14 2004 16:55:01

WTC2 FL82 - Baseline Temperature at 3600 sec

Diagonals: green

Seats: red Primary and bridging truss connections: blue Long-span and transfer truss connections: pink

Figure 5-96. User-defined break elements that failed by 60 min in the model of WTC 2

Floor 82 for Case Cj temperature condition.

NISTNCSTAR 1-6C, WTC Investigation 137
Chapter 5

Table 5-16. Number of failed user-defined break elements in the model of WTC 2

Floor 82 for Case Cj temperature condition.

Number of Break Elements

Web diagonals 381

Seats and gusset plates 46

Connections between primary and bridging trusses 70

Connections between long-span and transfer trusses 16

Total 513

Figure 5-97. Loss of vertical supports in Floor 82 of WTC 2 for Case Cj temperature

condition at 60 min (1x displacement magnification).

5.5.13 Results from Other WTC 2 Floors under Case Cj Temperature Condition

Table 5-17 gives the maximum vertical displacement of WTC 2 floors for Case C, temperature condition,

and Figs. 5-98 to 5-101 show the vertical displacements of WTC 2 floors when each floor experienced

the maximum displacement. Except for Floor 82, the maximum vertical displacement occurred in the

southeast area near the impact damage. The maximum displacement occurred at 60 min on all floors. The vertical displacement in the west office area was found to be insignificant on all the floors except

Floor 80 throughout the thermal loading because the insulation on floor trusses was intact in the west

office area. In Floor 80, the maximum vertical displacement of the west office area became about 20 in.

at 60 min.

Figure 5-102 (a) shows the average thermal expansion of floors at 60 min on each face, while

Fig. 5-102 (b) shows the average total thermal expansion of floors at 60 min in two orthogonal directions.

The total slab expansion ranged from 2.5 in. to 5.5 in. Figure 5-103 shows the horizontal reaction at each

column on the north and south faces of Floor 82. (The reaction force is positive when the floor pulls the

exterior column in.) It was found that Columns 353 to 359 were pulled in by the floor due to the

138 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

significant sag in the southeast area caused by the impact damage to the transfer truss and interior truss

seats in this area. Web diagonals of Floor 81 to Floor 83 buckled in the hot zones of the east office area where the

insulation on the trusses was damaged. Failures of the exterior truss seats, gusset plates, or seat bolts were not obser\'ed on Floor 79 to Floor 81. Trusses at Column 325 to Column 333 on the east face of

Floor 83 lost their \'ertical support at the exterior truss seats at 50 min, as shown in Fig. 5-104.

Table 5-17. Maximum vertical displacement of WTC 2 floors

for Case Cj temperature condition.

Floor Max. Displacement Time at the Maximum

(in.) (min)

79 19.0 60

80 30.1 60

81 31.0 60

82 45.2 60

83 38.9 60

(a) Entire model (b) Top view without slab

Figure 5-98. Vertical displacement of WTC 2 Floor 79 for Case C, temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

NiSTNCSTAR 1-6C, WTC Investigation 139
Chapter 5

J

(a) Entire model

AN

(in.

i

AN

(in.)

(b) Top view witliout slab

Figure 5-99. Vertical displacement of WTC 2 Floor 80 for Case Cj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure 5-100. Vertical displacement of WTC 2 Floor 81 for Case Cj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

140 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Entire model (b) Top view without slab

Figure 5-101. Vertical displacement of WTC 2 Floor 83 for Case Ci temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

84

83

82

80

79 ~

78

2 3 4 Slab Expansion (in)

(a) Average displacement of each face

84

83 -

82

80 -

79 -

78

—O— North-South —A— East-West

4 5 6 7

Total Slab Expansion (in)

(b) Average slab expansion in each direction

Figure 5-102. Average thermal expansion of WTC 2 floors at 60 min under Case Cj

temperature condition.

NISTNCSTAR 1-6C, WTC Investigation 141
Chapter 5

100

50

-200

—600 sec — 1,800 sec —3,000 sec

1,200 sec

2,400 sec

3,600 sec

140 130 120 Column ID

(a) West face

100

-150

360 350 340 330 320 Column ID

(b) East face

310

Figure 5-103. Horizontal reaction force per column of WTC 2 Floor 81 for Case Cj

temperature condition.

300

Figure 5-104. Loss of vertical supports in Floor 83 of WTC 2 for Case Cj temperature

condition at 60 min (3X displacement magnification).

5.5.14 Results from WTC 2 Floors under Case Dj Temperature Condition

Table 5-18 summarizes the maximum vertical displacement of WTC 2 floors under Case D, temperature

condition, and Figs. 5-105 to 5-109 show the vertical displacements of WTC 2 floors when each floor

experienced the maximum displacement. Due to the more extensive impact damage and higher

temperatures than Case Cj conditions, all floors had larger vertical displacement. Floor 80 and Floor 81

suffered impact damage to transfer trusses and many interior truss seats in the southeast area. Bridging

trusses that had been removed in the analyses with Case C, conditions were replaced in these two floors to provide support to the primary trusses in the east office area after aircraft impact. A maximum vertical

142 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

displacement of 97 in. occurred at Floor 81 near the impact damage at 50 min as shown in Fig. 5-107.

Similar sagging of the floor was found in other floors.

Gusset plates and bolts at more than 75 percent of all the exterior seats of the east face of Floor 82 and

Floor 83 failed due to horizontal shear force that was caused by the difference in the thermal expansion

between the floor and the exterior wall in the direction transverse to primary trusses. The truss at Column

357 of Floor 81 was the only truss that lost its vertical support at the exterior truss seat among all floors. This truss walked off the truss seat.

Floor sagging caused pull-in forces. For instance, Column 101 to Column 1 1 1 on the west face and

Column 347 to Column 359 on the east face were pulled in by the floor at 60 min on Floor 80 as shown in

Fig. 5-1 10 because of the floor sagging occurring in the southeast area. Since core columns were not

restrained in the horizontal directions, when the floor pulled in one face of exterior wall, the opposite face

of the exterior wall was also pulled in. Columns at the southeast comer were pulled in by the floor at Floor 79 and Floor 81. Many columns of the west face of Floor 82 were pulled in. The reaction forces at many columns of the east face of Floor 82 were close to zero, as shown in Fig. 5-1 1 1 (b). The gusset

plates and seat bolts failed at a number of trusses on the east face of Floor 82. Since columns at these

locations were not supported in the horizontal direction by the floor, the reaction force became close to zero at these columns.

Figure 5-112 shows the a\ erage thermal expansion of floors at 60 min of Case Dj temperature condition.

The average total floor expansion ranged from 1 in. to 5 in.

Table 5-1 8. Maximum vertical displacement of WTC 2 floors for Case Di temperature

condition.

Max. Displacement Time at the Maximum

Floor (in.) (min)

79 35.8 60

80 65.6 40

81 96.7 50

82 49.4 60

83 44.6 60

NISTNCSTAR 1-6C, WTC Investigation 143
Chapter 5

(a) Entire model (b) Top view witiiout slab

Figure 5-105. Vertical displacement of WTC 2 Floor 79 for Case Dj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

(a) Entire model (b) Top view without slab

Figure 5-106. Vertical displacement of WTC 2 Floor 80 for Case Dj temperature condition

at 40 min (downward displacement is negative; 5x displacement magnification).

144 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

(a) Entire model (b) Top view without slab

Figure 5-107. Vertical displacement of WTC 2 Floor 81 for Case Dj temperature condition

at 50 min (downward displacement is negative; 5x displacement magnification).

(a) Entire nnodel (b) Top view without slab

Figure 5-108. Vertical displacement of WTC 2 Floor 82 for Case Dj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

NISTNCSTAR 1-6C, WTC Investigation 145
Chapter 5

Figure 5-109. Vertical displacement of WTC 2 Floor 83 for Case Dj temperature condition

at 60 min (downward displacement is negative; 5x displacement magnification).

100

50 -

0

-

-50

oX

-100

-150

-200

—600 sec —1 ,200 sec —1,800 sec 2,400 sec

3,000 sec —3,600 sec

100

160 150 140 130 120 Column ID

(a) West face

110 100 360 350 340 330 320 Column ID

(b) East face

310 300

Figure 5-110. Horizontal reaction force per column of WTC 2 Floor 80 for Case Dj

temperature condition.

146 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

100

50

-50

O -100 oX

-150

-200

•

—600 sec —1,200 sec ; —1,800 sec —3,000 sec —2,400 sec - —3, 600 sec

100

160 150 140 130 120 Column ID

(a) West face

110 100

-200

- 600 sec

-1,800 sec

-3,000 sec

360 350 340 330 320 Column ID

(b) East face

-1,200 sec

2,400 sec

-3,600 sec

310 300

Figure 5-111. Horizontal reaction force per column of WTC 2 Floor 82 for Case Dj

temperature condition.

84

83

82

80

79

78

—o— North —O— South

East —X— West

1 2 3 Slab Expansion (In)

(a) Average displacement of each face

2 3 4 5 Total Slab Expansion (In)

(b) Average slab expansion in each direction

Figure 5-112. Average thermal expansion of WTC 2 floors at 60 min for Case Di

temperature condition.

NISTNCSTAR 1-6C. WTC Investigation 147
Chapter 5

5.5.15 Creep Effect

Full floor models were not run with creep due to the inherent convergence problems of BEAM188/189

elements under thermal loadings with materials with temperature-dependent creep. To evaluate the effect of creep, a simplified truss model at Colunm 333 of Floor 96 was extracted from the full floor model and was subjected to Case Bj temperature condition. The model was analyzed with and without creep in the

steel.

Vertical displacements at 40 min are shown in Fig. 5-113. The maximum displacements at 40 min were 44 in. for the model with creep and 26 in. for the model without creep. After 40 min, the model with

creep walked off the exterior truss seat, while the model without creep did not walk off the exterior truss

seat, and the vertical displacement increased with time and reached 31 in. at 100 min. The maximum

pull-in forces were 14 kip for the model with creep and 8 kip for the model without creep. The interface

force between the exterior columns and the truss became compression in the model without creep after 37 min because the thermal expansion overcame the shortening caused by the sagging.

Based on this study of the simplified truss model, creep in steel would significantly increase the existing

floor sag at high temperatures. Therefore, the sagging of floors was underestimated in the full floor

model analyses performed without creep.

AN

STEP-5

SUB =12 TIME=24nO

(in.)

NODAL SOLtTIO-J AN

(a) Model without creep (b) Model with creep

Figure 5-113. Vertical displacement of a simplified truss model at Column 333 extracted

from the full floor model of Floor 96 of WTC 1 under Case Bj temperature condition at 40 min (downward displacement is negative).

5.5.16 Effect of Column Boundary Conditions

The boundary conditions at the ends of columns and column length affect the horizontal force between

the floors and the exterior walls resulting from the thennal expansion of the floor. The fixed boundary

conditions and single story column length assumed in the floor analyses shown in this report represent a

relatively high degree of lateral restraint. The effect of reducing the degree of lateral restraint was

evaluated by performing nonlinear static finite element analysis with two story and three story column

lengths.

The results showed that the reduced restraint did not significantly affect the overall structural performance

of the floors although it decreased the vertical deflection of the floor by less than 20 percent and it

148 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

decreased the magniuide of the lateral force by as much as 85 percent. (Note that this decrease in deflection compensates partially for the additional deflection expected due to creep, as discussed in Section 5.5.15.)

5.5.17 Floor Subsystem in Global Models

Floor: The floors in the global models were modeled by SHELL181 elements with temperaturedependent elastic properties to enhance computational efficiency. Their functions were to:

1 . Simulate the diaphragm action of floors

2. Simulate the load transfer from the core to the exterior wall system when the core experiences

significant downward displacement due to shortening of core columns

The membrane stiffness of shell elements for the office area was detennined by calculating the

longitudinal stiffness of the composite floor using the single truss model which included not only the

stif&ess of the truss but also the stiffness of the connections between the truss and the exterior wall.

Fire-Induced Damage: Floors modeled by shell elements could not capture failure modes of floors under

ele\ ated temperatures: therefore, key failure modes were implemented in the global models at appropriate

points in time as fire-induced damage. Two different behaviors were considered based on conditions of

connections between the floor and the exterior wall: 1) the floor sagged and pulled the exterior wall in and

2) the floor was disconnected from the exterior wall. The locations of floor/wall disconnections and the

locations and magnitudes of pull-in forces in the sagging floor areas were determined using not only the

full floor model results but also the actual observations from photographs and videos and the analyses

performed on isolated exterior wall models, as discussed in Section 2.5 of NIST NCSTAR1-6D.

Results from the full floor model analyses are presented in Figs. 5-1 14 to 5-117 only at the end of time

histories for the conditions of the connections between the exterior wall and the floors. The figures show

the following conditions:

• Condition 1 : gusset plate failure + seat failure due to vertical shear (loss of vertical support)

• Condition 2: gusset plate failure + seat bolt shear-off + truss walk-off (loss of vertical

support)

• Condition 3: gusset plate failure + seat bolt shear-off + significant vertical displacement (>25

in.) of the floor in that area (floor remains vertically supported)

• Condition 4: tensile force between the exterior wall and the floor system (floor remains

vertically connected, but exerts pull-in force on the exterior wall)

Conditions 1 and 2 were treated as the case of floor/wall disconnections. Conditions 3 and 4 were treated

as the case where the floor pulled in the exterior wall. Owing to the failure of the gusset plate and seat bolts (Condition 3), the floor in this model cannot pull in the exterior wall at these connections. In reality,

in addition to studs and diagonal strap anchors that may not have failed, there was friction between the

truss bearing angles and the exterior truss seat angle. For these reasons. Condition 3 was treated as the case where the floor pulled in the exterior wall. More discussion on the pull-in force can be found in Section 2.5 of NIST NCSTAR1-6D.

In the full floor model, every other exterior column was connected to the floor because spandrel studs and

strap anchors were removed from the model. The four conditions above were defined for columns at primary trusses; however, they are shown in Figs. 5-1 14 to 5-117 for all columns because there were

NISTNCSTAR 1-6C, WTC Investigation 149
Chapter 5

strap anchors connecting the floor to the columns located between primary trusses. When the same

condition of the comiection was found for two adjacent truss locations, the column between the two

tmsses was assumed to have the same condition as the adjacent columns in these figures. For example,

failure of exterior seats (Condition 1) occurred at Columns 329 and 331 of Floor 98 of WTC 1 for Case Bj

temperature condition, hi Fig. 5-115, Column 330 is also indicated as Condition 1, although there was no

truss located at Column 330.

150 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

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154 NISTNCSTAR 1-6C, WTC Investigation
Full Floor Subsystem

5.5.18 Summary of Results and Discussion

The behaviors of the floor system found in the full floor models subjected to impact damage and elevated

temperatures from the fires can be summarized as follows:

Bridging trusses subjected to elevated temperatures buckled between primary trusses. When significant differences in thermal expansion of the floors and exterior walls in the direction transverse to the axes of primary trusses occurred near the comers, studs, diagonal strap

anchors, gusset plates, and seat bolts at exterior truss seats failed due to the lateral shear. Web diagonals of floor trusses with damaged insulation buckled.

Floors sagged as they lost bending stiffness resulting from web diagonal buckling, and they

pulled the exterior wall in.

Truss seats disconnected from the exterior walls.

Pull-in forces were expected to develop whenever the floor sagged. Although the floor sagging was

capmred by the floor models in the heated area, the pull-in force on the exterior columns was not captured

in most of the full floor model analyses. To accurately calculate pull-in forces between the floors and the

exterior columns in the full floor model, much more detailed modeling will be required. Such modeling

includes accurate boundary conditions on columns, creep in steel, friction at the truss seats, accurate

evaluation of failure of strap anchors and studs, and concrete cracking and spalling. In addition,

temperature time histories that were used in the full floor model analyses may have been conservative

estimates, which were derived from conser\'ative estimates of impact damage to the insulation. Further

discussion on the pull-in force can be found in Section 2.5.2 of NiST NCSTAR1-6D.

NISTNCSTAR 1-6C, WTC Investigation 155
Chapter 5

\

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156 NISTNCSTAR 1-6C, WTC Investigation
Chapter 6

Exterior Wall Subsystem

6.1 OBJECTIVE

The objective of the exterior wall subsystem model was to study the performance of the exterior wall

subjected to the combined effects of gravity and thermal loads for the following conditions:

• all floors provide lateral support,

• two adjacent floors do not provide lateral support,

• three adjacent floors do not provide lateral support,

• in addition to loss of lateral support at three floors, the exterior wall is subjected to pull-in

forces by the sagging floors, and

• m addition to loss of lateral support at three floors, the exterior wall is subjected to additional

gravity loads.

The following temperamre-dependent nonlinearities and material properties were included in the exterior

wall model:

• Large deflections and buckling

• Material plasticity

• Creep

• Material failure

• Column splice failure

• Spandrel splice failure

6.2 EXTERIOR WALL SUBSYSTEM DESCRIPTION

The exterior walls of the towers were constructed with prefabricated wall panels, referred to hereafter as

panels. Typical panels contained three-column segments spanning three stories with three spandrels

extending one half-span past the outer columns. The panels were arranged such that the spandrel splices

between panels aligned vertically, and the column splices between panels were offset by one story.

The modeled exterior wall subsystem was located on the north face of WTC 1 toward the east side and

included nine columns, extending vertically from the column splice located below Floor 91 to the column

splice above Floor 99, and nine spandrels extending horizontally from the spandrel splice between

Columns 149 and 150 to the spandrel splice between Columns 158 and 159. This exterior wall subsystem

model included seven full panels and portions of four other panels.

Figure 6-1 shows the subsystem pictorially. Figures 6-2 (a) and 6-2 (b) give the types and yield

strengths of the columns and spandrels and the types of column and spandrel splices. Figure 6-3 shows

the column plate notation used. Tables 6- la through 6-lc give the geometry and material properties of

the plates in the columns, the spandrels, and the column and spandrel splices.

NISTNCSTAR 1-6C, WTC Investigation 157
Chapter 6

/'\

[5, i?') iie/

-J

p ® S ^

!^ ?^ p

S

Figure 6-1. Exterior wall subsystem structure.

The odd-numbered columns supported the floor trusses. Pairs of strap anchors extended diagonally from

the top chords of truss pairs to the even-numbered columns. The trusses and the strap anchors partially

braced the columns both in-plane and out-of-plane of the exterior wall.

158 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

Column -150 151 152

Floor - 99

98

97

96

95

94

93

92

91

r

153 1

10

CO !0 0

CM 0

154 155 156 157 158

<11 ^^1411

4211

i "Zl. 4.21 j431 XXX-XX indicates type and nominal yield strength of column (ksi] XXX indicates type of colum splice

(a) Columns and column splices

Column- 150 1 51 162 153 1 54 1 55 156 1 57 1 58

I

Floor - 991^

I

98!^

97?£2-

95^

9411^

I

931:^

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9l|^

45

50

45

45

45

42

•45

42

45

46

50

45

46

50

-45

46

50

50

55

55

60

60

65

70

70

"2

XX indicates nominal yield strength of spandrel (ksi) XXX indicated type of spandrel splice

Spandrel thickness is 3/8 in.

(b) Spandrels and spandrel splices

Figure 6-2. Columns, spandrels, and splices: type and material assignments.

NISTNCSTAR 1-6C, WTC Investigation 159
Chapter 6

ECRL

Plate 1

14"

Plate 2

Plate 1

Plate 3

4.5"

6.5"

13.5"

Spandrel---''^

Figure 6-3. Schematic of column cross section.

Table 6-1a. Column sectional properties.

Plate 1 Plate 2 Plate 3. Column Ixt Ixt 1 X t Type (in. X in.) (in. X in.) (in. X in.)

120 13.5 X 0.25 13.5 X 0.25 15.75 X 0.25

121 13.5 X 0.3125 13.375 X 0.25 15.75 X 0.25

1 22 13.5 X 0.375 13.25 X 0.25 15.75 X 0.25

123 13.5 X 0.4375 13.125 X 0.25 15.75 X 0.25 124 13.5 X 0.5 13 X 0.25 15.75 X 0.25

125 13.5 X 0.5625 12.875 X 0.25 15.75 X 0.25

'All spandrels in model are 52 in. deep x 3/8 in. thick.

Table 6-1b. Column splice details.

Column

Splice Type

Butt Plate

Thickness

(in.) Numberof Bolts

Bolt Diameter

(in.)

Gage

(in.)

Bolt Spacing

(in.) ColumnSplice ID

411 1.375 4 0.875 3.5 6 411

421 1.625 4 0.875 3.5 6 421

431 1.875 4 1 3.5 6 431

Butt plates have specified yield strength of 50 ksi. -Bolts are A325.

160 NISTNCSTAR 1-6C. WTC Investigation
Exterior Wall Subsystem

Table 6-1 c. Spandrel splice details.

Spandrel

Splice

T^pe

Number

of

Bolts/Row

Total

Number

of Rows

Bolt

Spacing

fin 1

Gage

(in )

Overall Splice Plate Dimensions

(in \ in \ in ^

Bolt to Centerline

of Splice

fin )

Gap B/VV

Spandrels

(in

)

Spandrel

Splice

ID

101 6 5 (a 9 49x6.75x.25 1.875 0.75 101

102 8 3.6.3@:9.6,3 49x6.75x.25 1.875 0.75 102

111 6 4 5(g9 3 49x12. 75X.25 1.875 0.75 111

112 8 4 3.6.3(29.6,3 3 49xl2.75x.25 1.875 0.75 112

'All spandrel splices use 7/8 in. A325 bolts; specified spandrel splice plate yield strength is 36 ksi. "Holes in spandrel are 14 in. larger than bolts; holes in plates are boh +1/16 in. or option to match spandrel holes.

6.3 FAILURE MODES

The exterior wall subsystem model can capture the following failure modes:

• Column buckling from large lateral deformations,

• Column buckling from loss of support at floor truss seats and strap anchors,

• Failure of column splice bolts, and

• Failure of spandrel splice boUs or tearing of spandrel or splice plates at boh holes.

The model does not capture the local buckling of column plates or the formation of plastic hinges

(kinking) from the interaction of local plate buckling and general stability of the column when subjected

to combined axial load and bending moments.

Several of the later analyses did not include the effects of creep. Displacement control analysis in ANSYS did not ftinction properly when strain rate effects of creep were included.

6.4 MODEL VALIDATION

6.4.1 Description of Models

Validation of the exterior wall model was performed by comparing the stiffness of an ANSYS model of a

single exterior wall panel with beam and shell elements to a SAP2000 shell model of the same panel

developed by Leslie E. Robertson Associates under a contract from NIST.

Figure 6-4 shows the SAP2000 shell model of a typical prefabricated panel at Floors 79 to 82 provided

by NIST. The model was modified as follows:

1. Eliminated self-weight from loading conditions.

2. Provided a stiff member at the top of the columns.

3. Added out-of-plane wall supports (UY) at the top of the columns for stability under out-ofplane loading.

Figure 6-5 shows the ANSYS prefabricated panel model. BEAM 189 elements modeled the columns,

SHELL181 elements modeled the spandrels, and BEAM4 elements connected nodes on the axis of the

columns to nodes located in the mid-plane of the spandrels.

NIST NCSTAR 1-6C, WTC Investigation 16:
Chapter 6

Figure 6-6 shows the various boundary conditions. Out of plane displacement (UY) was restrained at the

tops of the columns. All tliree directions of translation were restrained at the bottoms of the columns.

The spandrels were free at the boundaries of the model.

Both models were subjected to three loading cases at room temperature, as shown in Fig. 6-6:

1 . A vertical force (FZ) at the top of one of the outside columns.

2. A horizontal force in the plane of the wall (FX) at the top of one of the outside columns. The

stiff members described previously distributed this shear load evenly to the tops of all three

columns.

3. A transverse force (FY) on the middle column at Floor 81 (middle floor).

The loads described above did not include self-weight.

Figure 6-4. SAP2000 model of prefabricated panel.

162 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

46 in

52 in.

92 in

-Rigid truss members to transfer horizontal forces

t = 0.4375 in., typ

10 elements between spandrels

9 elements deep, 4 elements

between columns

t = 0.4370 in. at columns,

2 elements wide

20 in.

Figure 6-5. ANSYS model of prefabricated panel showing meshing.

lateral (100 k)

out-of-plane /

(10 k) ^

vertical (10 k)

UY supports at top, typ.

UX,UY,UZ supports at base, typ.

Figure 6-6. ANSYS model of prefabricated panel showing boundary conditions and

loading (loads applied separately).

NISTNCSTAR 1-6C, WTC Investigation 163
Chapter 6

6.4.2 Validation Results

Figures 6-7 through 6-9 show deflected shapes and indicate the displacement at the points of applied load

for the SAP2000 and ANSYS models. Table 6-2 summarizes the differences in reactions and

displacements between the SAP2000 and ANSYS models. The table indicates that these differences were

small.

UX = 2.91 in.

UX = 2.91 in.

UX = 2.90 in.

2.91 in.

At Top of Loaded Column

Ave SAP2000: 2.91 in. ANSYS e.g.; 2.70 in UX difference: 7.3%

UX = 2,70 in.

/

i I

SAP2000 Deflected Shape ANSYS Deflected Shape

Figure 6-7. Deflection of prefabricated panel under 100 kip lateral load.

Uy = 0,519 in.

UY = 0,520 in.

UY = 0,519 in.

UY = 0,520 in.

UY = 0.588 in.

/ t

At Point of Applied Load

Ave SAP2000 0.520 in. ANSYS eg: 0.588 in. UY difference: -13 0%

/ ///

SAP2000 Deflected Shape ANSYS Deflected Shape

Figure 6-8. Deflection of prefabricated panel under 100 kip transverse load.

164 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

UZ = -0.00582 in. —>kI

UZ = -0.00517 in.

UZ = -0.00658 in.

UZ = -0,00595 in.

U2 = -0.00516 in.

At Top of Loaded Column

Ave SAP2000: -0,00591 in. ANSYSc.g.: -0.00516 in, UZ difference: -4.2%

SAP2000 Deflected Shape ANSYS Deflected Shape

Figure 6-9. Deflection of prefabricated panel under 10 kip vertical load.

Table 6-2. Pre fabricated panel validation results.

SAP2000/ANSYS Difference Range

Loading Condition Reactions' Displacements"

Lateral FX RX: -2%to+l% UX: 7%

Trans\ erse FY RY: -6% to +7% UY: -13%

Vertical FZ RZ: -l%to+2% UZ: -7%

Range considers maximum disparities between results for all support

reactions. "Displacements considered at tops of columns for FX and FZ, and at points of load application for FY.

6.5 FINITE-ELEMENT MODEL OF EXTERIOR WALL SUBSYSTEM

6.5.1 Elements and Meshing

Figure 6-10 shows the model in elevation. BEAM 189 elements modeled the columns. Above and below

spandrels, BEAM189 elements modeled the complete cross sections of the columns. At spandrels,

BEAM 189 elements modeled cross sections where the interior plate thickness of the column was reduced

to 0.005 in. to maintain a closed section yet allowed for a continuous spandrel. Since neutral axis location

of column shifted in the column elements in the spandrel zone, MPC184 rigid elements were used to connect the neutral axes of column elements where this shift occurred. SHELL181 elements modeled the

spandrels. Figure 6-1 1 shows the number of elements used to model columns and spandrels. BEAM4

elements connected nodes on the axis of the columns to nodes located in the mid-plane of the spandrels.

Figure 6-12 shows this use of the BEAM4 elements.

BEAM4 elements are two-node Euler (elastic) elements with large deflection capability. BEAM 189

elements are three-node (quadratic) Timoshenko beam elements with large deflection, plasticity, and

creep capabilities. SHELL181 elements are four-node multi-layer elements with large deflection.

NISTNCSTAR 1-6C. WTC Investigatiori 165
Chapter 6

plasticity, and creep capabilities. MPC184 elements are multipoint constraint elements that implement

kinematic constraints using Lagrange multipliers. These element types and their features are summarized

in Table 4-1.

Material IDs, as described in Chapter 3, were assigned to the elements. The properties (e.g. stiffness) and

behavior (e.g. plasticity) of the elements vary with temperature as the assigned material properties vary

with temperature.

6.5.2 Boundary Conditions

The bottoms of all columns in the model were restrained in the vertical direction. The top and the bottom

of all columns in the model were restrained in the direction normal to the wall. In addition, the bottom of

central Column 1 54 was restrained in the in-plane horizontal direction. Symmetry boundary conditions were imposed on the spandrels at the boundaries of the model, except that the spandrels were free to expand in the plane of the wall. Motion out of the plane of the wall was restrained at all floor truss seats and strap anchors. In several analyses, such restraints were removed at two or three floors (either Floors

95 and 96 or Floors 95, 96, and 97) to investigate the effect of floor sagging and floor/wall disconnection on stability of the exterior wall system.

40 in. typ.

Floor 99

UY supports at top, typ.

ROTY and ROTZ

supports at spandrel

edges, typ.

UY support at seats - each

column, each floor, typ. unless

floors specifically unrestrained

UY,UZ supports, typ. —^

'— UX,UY,UZ support at middle column

Figure 6-10. Exterior wall subsystem model with boundary conditions.

166 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

10 elements

through depth

4 elements

each side of splice

SHELL181

elements for spandrels

BEAM189

elements for columns

si SB

li II

g |S mmmm

mm m m m m m

ms m

w» m

J4-

2 elements at columns

4 elements

betvjeen

columns, typ.

17.33 in. (gusset plaie)

25.5 in. (center

of stand-off)

Column

splices

1 element at spandrel

splice

Figure 6-11. Typical meshing of exterior wall model components.

r- Plate 2

t=0.25 in.

Plate 1

-

t varies

Plate 4

1=0.005 in.

At spandrels

Plate 1

t varies

Stiff BEAM4 elements

in "V" or "T" patterns

attach spandrel to column e g to create

composite action

between column and

spandrel.

Plate 1

t varies

r

Plate 2

t=0.25 in.

Plate 1

t varies

Plate 3

t=0.25 in.

Away from spandrels

Figure 6-12. Schematic representation of columns used in the exterior wall model.

NISTNCSTAR 1-6C, WTC Investigation 167
Chapter 6

6.5.3 One-, Two-, and Three-Story High Columns

Figure 6-13 shows the model of a one-story high exterior column. The model included a one-story high

portion of Column 1 5 1 extending from Floor 95 to Floor 96 and portions of spandrels at Floor 95 and

Floor 96. The model also represented Column 151 from Floor 96 to Floor 97 since the dimensions, plate

thicknesses, and material properties were identical to those of Column 151 from Floor 95 to 96. SHELL181 plate elements modeled the plates of columns and spandrels. CERIG rigid elements

connected the center of gravity of the column to its component plates and to the spandrel at both the top

and the bottom of the model. The column was pinned at the bottom and restrained in the two horizontal

directions at the top. Axial displacement was applied incrementally at the top of the model.

Figure 6-14 shows the variation of axial load with the imposed axial displacement and the resulting

lateral deflection at room temperature (RT) and 700 °C. This figure also shows the hand calculated

theoretical column load levels at room temperature (RT) and 700 °C for:

1. Local buckling of Plate 2 and Plate 3.

^

2. Unifonn yielding of the column.

3. Axial load demand due to gravity dead and hve loads at Floor 96.

Figure 6-15 shows the local bucking deformation of Plate 2 and Plate 3 at the maximum load at room

temperature. Figure 6-16 shows a plastic hinge at mid-height of the column for an imposed axial

displacement of 2 in. Figure 6-17 shows local buckling in Plate 2 and Plate 3 at maximum load at 700 °C.

Figure 6-14 shows that at room temperature Plate 2 and Plate 3 buckle locally at a load that is less than

the maximum column load, but at 700 °C the column yields before it buckles locally. This figure also

shows that the expected column demand load of 175 kip is substantially lower than the local buckling

load at room temperature and the column yield load at 700 °C.

At room temperature, the load-carrying capacity in the post-buckling regime decreased rapidly; however,

it decreased much more gradually at 700 °C.

Axial load-displacement behaviors of two- and three-story models were also examined, and the results are shown in Fig. 6-14. As the unsupported length became longer and the temperature became higher, the

negative slope of the axial load-deflection curve in the post-buckling regime became less steep.

168 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

DISPLACEMENT

STEP=1

SUB =1 TIHE=1

DMX =.505E-12

ANSYS

MAR 29 2004

13: 49:28

Figure 6-13. One-story exterior column model.

1225

1050

Axial yield load of column at RT =1177 Kip

Elastic local buckling load for 1-story high column at RT =1004 Kip

• 1 -Story (RT)

1 - story (700C)

•2-Story (RT)

2-Story (400C)

•3-Story (RT)

0.0 0.5 1.0 1.5 2.0 Vertical Displacement (in)

2.5 3.0

Figure 6-14. Load-deflection of column at room temperature and 700 °C.

NISTNCSTAR 1-6C. WTC Investigation 169
Chapter 6

DISPLACEMENT

STEP=3

SUB =34 TIME = 1. 346

DMX =. 36137

ANSYSI

MAR 2 200 4 14:27: 10

Figure 6-15. Local buckling of column at room temperature.

DISPLACEMENT

STEP=4

SUB =200

TIME=3

DMX =9.169

ANSYS

MAR 2 2004

14 : 31: 48

DISPL. UP TO 2in

Figure 6-16. Plastic hinge in column at room temperature.

170 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

DISPLACEMENT

STEP=4

SUB =234

TIME=2. 173 DMX =.234252

ANSYS

MAR 2 9 2004

13: 45: 08

6.5.4

Figure 6-17. Deformed shape of column at maximum axial load at 700 °C.

Spandrel Splices

Figure 6-18 shows the typical layout of the spandrel splices in the model. User-defined break elements were used to model the interior spandrel splice connections, and nodal couples were used to model the

exterior spandrel splice connections. An interior spandrel splice occurs between Columns 150 and 158,

and an exterior spandrel splice occurs at the edges of the model outside of Columns 150 and 158. Figure

6-19 shows the modeling of an interior spandrel splice. User-defined break elements at each node

through the depth of a spandrel allowed the model to capture connection failure modes including ( 1 ) bolt

shear, (2) tearing of the spandrel plate, and (3) tearing of the splice plates at the bolt holes. The exterior

wall model contains 18 interior spandrel splices with 1 1 break elements at each sphce for a total of

1 98 spandrel splice break elements. With initial and failure stiffness values and temperature-dependent

capacities defined by the user, the user-defined break elements transfer forces and moments between

nodes according to the initial stiffness values until the element reaches its capacity in one direction. Upon

reaching the capacity in one direction, the stiffness of the element in all directions changes to the

corresponding failure stiffness, and the element sheds load to other load paths. The models used user- defined break elements that had the capability to fail in translation or rotation.

NISTNCSTAR 1-6C, WTC Irivestigation 171
Chapter 6

Figure 6-18. Typical spandrel splice layout for exterior wall subsystem.

Spandrel

continues

Y

X

Spandrel

continues

Coincident nodes and

break elements

Figure 6-19. Modeling of a typical interior spandrel splice in the exterior wall model.

172 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

6.5.5 Column Splices

Two BEAM189 elements for each of the four bohs, four pairs of CONTA178 contact elements at the

faying (contact) surfaces, and stiff BEAM4 elements connecting the tops of the bolts to the CONTAI78

contact elements were used to model the column splice. COMBIN37 elements modeled the fracture of

the column splice bolts based on data from bolt tests provided by NIST and on shear failure of the splice.

Figure 6-20 shows a schematic view of the column sphce. A coefficient of friction of 0.35 was used for the contact elements. The 7/8 in. diameter column splice bolts were preloaded to 36.05 kip at 20 °C

(AISC 1964).

The column splice model cannot fail in compression. In tension, the bolts and , therefore, the entire splice

will disconnect at 0. 18 in. deflection beyond the ultimate capacity of the bolts. In shear, the column

splice will disconnect after 1.1 in. deflection. The shear capacity is the summation of bolt shear capacity

and splice friction. In bending, the capacity is controlled by bolt tension. The peak moment capacity occurs prior to failure of the first set of bolts with some capacity remaining on the second set of bolts.

The column splice model was verified by subjecting it to three displacement controlled load cases under

two temperature conditions and comparing the results with hand calculated maximum capacities for each

case. The load cases examined were: axial extension, to determine a maximum tensile load; applied

rotation with 175 kip axial compression, to determine a maximum moment; and applied lateral displacement with 175 kip axial compression, to determine a maximum shear. Each load case was

performed at 20 °C and 300 °C. The maximum difference between the finite element model and

calculated capacities was 4 percent under the tensile load case. All other cases showed agreement to within 2.5 percent. The load-displacement response of the splice model to each load case was in agreement with the predicted behavior.

Column above with COMBIN37 break elements that connect column to splice

Stiff BEAM4 elements

CONTA178 contact element

BEAMI 89 for bolt tension -

BEAM44 for shear stability -

contact elements

Column Cross Section

Not to Scale

Figure 6-20. Column splice model used in exterior wall model.

NISTNCSTAR 1-6C, WTC Investigation 173
Chapter 6

6.5.6 Loads

The loads on the model were applied sequentially in the following order:

• Self weight of the exterior wall components,

• Column splice bolt preload,

• Gravity dead and live loads of the floor system,

• Temperature time histories provided by NIST, and

• Transverse pull-in force from sagging floors or additional vertical load from a potential

redistribution of gravity loads to this portion of the exterior wall

Gravity Loads

Gravity loading was obtained from two sources: the LERA SAP2000 global model and the LERA

SAP2000 floor model. To capture the gravity load effects from upper floors (those above Floor 99),

internal forces and moments at midheight of the columns between Floors 99 and 100 in the LERA

SAP2000 global model, caused by dead plus 25 percent of design live load, were applied as loads at the

tops of the corresponding coluimis in the exterior wall model at the center of gravity of the columns. To

capture the gravity load effects from individual floors, floor loads were extracted from the LERA

SAP2000 floor model and applied to each column. Also, a moment about the plane of the wall, based on

the vertical force from the floor and the eccentricity of the truss seats, was applied to each odd-numbered

column at the mid-plane of the spandrel.

Thermal Loads

To represent a range of thennal conditions expected in the WTC towers, NIST provided five thermal load

conditions based upon fire conditions in the towers. These were labeled D, DBARE, E, El 19, and F, and

are described in Table 6-3. These load conditions differed in fire behavior, intensity, location in the

towers, and time. Thennal load DBARE assumed steel without thermal insulation. Thennal load El 19

corresponded to the standard ASTM-El 19 fire load. Figure 6-21 shows how the maximum temperature

in each thermal loading condition varied with time.

For columns that were modeled by BEAM189 elements, temperatures were provided for nodes at the center of gravity of the column, and their linear gradients transverse to the exterior wall were also

provided. Gradients parallel to the wall were found to be negligible. Temperatures for SHELL181

elements were provided at each node. NIST did not always provide temperatures for the bolts at column

splices. When bolt temperatures were provided, they matched temperatures at the nearest interior or

exterior tips of columns.

174 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

Table 6-3. Thermal loadinc conditions used in the exterior wall model.

Therinal

Loading

Condition

Building and

Location Columns Floors

Thermal

insulation

Time

Duration

Maximum

Temperature °C

D WTC 1 South face tow ards West

340 - 348 91-99 as specified 90 mm 537 °C

WTC 1 Same as D

340-348 91-99 none - bare

steel

90 min 598 °C

E WTC 1 East face towards North

221 - 229 91-99 as specified 90 min 871 °C

£119 WTC 1 as specified 90 min 418 °C

F WTC 2 North face East comer

250-258 76-84 as specified 60 min 382 °C

NISTNCSTAR 1-6C, WTC Investigation 175
Chapter 6

Transverse Pull at Disconnected Floors

When floors sag, they begin to pull in the columns. The results of truss component analyses indicated

approximately 14 kip of pull-in force per truss. Strap anchors distributed this pull to the columns that did

not support trusses. A 15 kip pull-in force was applied to each column of laterally-unsupported floors to model the effect of the sagging floor.

Push-down Loading

Exterior wall columns were subjected to additional gravity loads that were redistributed due to weakening

of other exterior walls and/or the core by the aircraft impact or temperature effects through the hat truss and spandrels. To simulate a redistribution of gravity loads, equal vertical displacements were imposed at the top of each column to push the model down. The imposed vertical displacements induced additional

gravity loads in the columns.

6.6 ANALYSIS CASES

The loading sequence described in Section 6.5.6 is the same for all exterior wall analyses. Table 6-4

summarizes the different loadings and boundary conditions of the exterior wall subsystem.

As shown in Table 6-4, Case 6 and Case 7 used thennal condition DBARE with two and three floors not bracing the exterior wall system. Case 8 used DBARE, where the columns were not braced at three

floors, and transverse loads (pull-in forces) were applied. Case 9 used DBARE, where the columns were

not braced at three floors and vertical displacement was applied to the top of each column until unloading

of the columns and instability was detected.

The analyses of Case 1, Case 5, and Case 6 through Case 9 were completed for the entire temperature

time history of each case provided by NIST. The analysis of Case 2 was inadvertently stopped at 83 min

of its temperature history; the temperature time history at 83 min was flat, and no significant change in the results was expected. Case 3, at 70 min of its temperature history, reached a temperature of 800 °C,

beyond which material properties were not defined, and the computation was terminated. Case 4 could

not be advanced past 83 min of its temperature time history, because the creep algorithm failed. The

temperature difference between the temperatures at 83 min and 90 min was not significant for this case.

176 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

Table 6-4. Analysis cases for exterior wall subsystem model.

Analysis

Case

Thermal

Loading

Bolt

Temperatures

Creep

Effects Floor Supports

Pull-in Force

Push

Down

1 U No Yes A 11 All

-> UrSAKh INo Yes A n

All E Yes Yes All 4 E119 No Yes All

5 F No Yes All

6 DBARE Yes Yes All but 95 and 96

7 DBARE Yes No All but 95,96,

and 97

8 DBARE Yes No

All but 95, 96,

and 97

X

9 DBARE Yes No

All but 95, 96,

and 97

X

6.7 ANALYSIS RESULTS

6.7.1 Columns Braced at All Floors

This group of analyses includes Analysis Case 1 through Case 5.

Analysis Case 1 (Fire Scenario D) Figures 6-22 (a) through 6-22 (c) show the total displacement, von

Mises stress, and plastic strain, respectively, for the entire model. Figure 6-22 (a) shows that the

maximum displacement of 1.53 in. occurred at Floor 98 near Column 158. Figure 6-22 (b) shows that the

maximum von Mises stress in the spandrels of 49 ksi occurred at Floor 95 and Column 156. Figure 6-22

(c) shows that plasticity in the spandrels was confined to Floors 95 and 96, with the highest plastic strain occurring at Floor 96 near Column 155. Figure 6-22 (d) shows the deformation of the spandrel at Floor 94. Table 6-5 summarizes the status of the spandrel sphce break elements. All failed break

elements indicated tearing failure.

NISTNCSTAR 1-6C, WTC Investigation 111
Chapter 6

(a) Total deflection (b) von Mises stress

czLzizn

RjTPW' 1

(c) Plastic strain

aart s.£

J5!33t!<4

g .6SS,-03

(in ./in.)

ii J»T(n;3C

If^7^1

PCX -i.A^S

'.^ »SM.3i6

'.Til -2

50X1 displacen^ent fnagnification

(d) Spandrel deformation at Floor 94

Figure 6-22. Structural response for temperature time history D with all floors

supported.

Table 6-5. Summary of spandrel splice break elements for

Number of failed elements

Floor West Interior Splice East Interior Splice

99 3 3 98 0 0

97 2 1 96 1 2 95 0 0

94 0 0 93 0 0

92 0 0

91 0 0 Total 6 6

178 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

Analysis Case 2 (Fire Scenario DBARE) Figures 6-23 (a) through 6-23 (c) shows the total displacement, von Mises stress, and plastic strain, respectively, for the entire model. Figure 6-23 (a) indicates the

maximum displacement of 3.74 in. occurred at the top of Column 158. Figure 6-23 (b) shows that the

maximum von Mises stress in the spandrels of 49 ksi occurred at Floor 94 and Column 156. Figure 6-23

(c) shows plastic strain in spandrels at Floors 94 through 98, with the highest value at Floor 95 and

Column 152.

Table 6-6 summarizes the status of the spandrel splice break elements. All failed break elements

indicated tearing failure.

JOE » 2!t9i;

^ ,asut

U < I M I M

i 1 5151

(a) Total deflection (b) von Mises stress

iiiiitiii

IIFiittM

am e.i

JIB S 2!KK

t»crr-!

(in./in.)

(c) Plastic strain

Figure 6-23. Structural response for temperature time history DBARE with all floors

supported.

NISTNCSTAR 1-6C. WTC Investigation 179
Chapter 6

Table 6-6. Summary of spandrel splice break elements for temperature time history

DBARE with all floors supported.

Number of failed elements

Floor West Interior Splice East Interior Splice

QQyy

A

u

•J OSyo 1jS 07y 1

1111 OA u A

U

yj 0 0

94 0 {) 93 0 0

92 0 0

91 0 0

Total 4 7

Analysis Case 3 (Fire Scenario E) Figures 6-24 (a) through 6-24 (c) show the total displacement, von

Mises stress, and plastic strain, respectively, for the entire model. Figure 6-24 (a) shows that the

maximum displacement of 1.87 in. occurred at Floor 99 near Column 158. Figure 6-24 (b) indicates that the maximum von Mises stress in the spandrels of 57 ksi occuired at Floor 94 between Columns 156 and

157. Figure 6-24 (c) shows that plastic strain occuired in spandrels at Floors 94 through 96, with the

highest value occurring at Floor 94 between Columns 154 and 155. Figure 6-24 (d) shows the

deformation of the spandrel at Floors 94, 95, and 96. Table 6-7 summarizes the status of the spandrel

splice break elements. The nature of the break element failures indicated tearing failure at Floors 97 and

above, boh shear failure at Floors 95 and below, and a combination of tearing and bolt shear failure at Floor 96.

180 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

(a) Total deflection (b) von Mises stress

-'92.e!5f.

(c) Plastic strain

iQX displacemei^t magnification

(d) Spandrel deformation at Floors 94 through 96

Figure 6-24. Structural response for temperature time history E (hot bolts)

with all floors supported.

Table 6-7. Summary of spandrel splice break elements for

Number of failed elements

Floor West Interior East Interior Splice

99 3 3 98 3 3 97 2 2 96 8 8 95 2 11 94 1 2 93 0 0

92 0 0

91 0 0

Total 19 29

NISTNCSTAR 1-6C, WTC Investigation 181
Chapter 6

Analysis Case 4 (Fire Scenario El 19) Figure 6-25 (a) through 6-25 (c) show the total displacement, von

Mises stress, and plastic strain, respectively, for the entire model. Figure 6-25 (a) shows that the

maximum displacement of 2.07 in. occurred at Floor 99 near Column 158. Figure 6-25 (b) indicates that maximum von Mises stress in the spandrels of 53 ksi occurred at Floor 94 and Column 158. Figure 6-25

(c) shows plastic strain in spandrels between Floors 93 through 99, with the highest value occurring at Floor 93 between Columns 154 and 155. Figure 6-25 (d) shows the defonnation of the spandrel at Floor

93. Table 6-8 summarizes the status of the spandrel splice break elements. All failed break elements

indicated tearing failure.

(a) Total deflection

(c) Plastic strain

(in ./in.)

Sm 14 iOOA

T£5E«500I>

iiiiiii

mm

(psi)

(b) von Mises stress

(d) Spandrel deformation at Floor 93

Figure 6-25. Structural response for temperature time history E119

with all floors supported.

182 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

Table 6-8. Summary of spandrel splice break elements for

Number of failed elements

Floor \\ est Interior East Interior Splice

99 3 3 98 0 0 97 0 0 96 0 0 95 0 0 94 0 0 93 0 0 92 0 0

91 0 0

Total 3 3

Analysis Case 5 (Fire Scenario F) Figures 6-26 (a) through 6-26 (c) show the total displacement, von

Mises stress, and plastic strain, respectively, for the entire model. Figure 6-26 (a) shows that the

maximum displacement of 1.57 in. occurred at Floor 99 near Column 158. Figure 6-26 (b) indicates that the maximum von Mises stress in the spandrels of 46 ksi occurred at Floor 96 and Column 158. Figure

6-26 (c) shows plastic strain in spandrels betw^een Floors 96 through 99 with the highest value occurring

at Floor 97 at Column 151. Figure 6-26 (d) shows the deformation of the spandrel at Floor 99. Table 6-

9 summarizes the status of the spandrel splice break elements. All failed break elements indicated tearing

failure.

NISTNCSTAR 1-6C. WTC Investigation 183
Chapter 6

(a) Total deflection (b) von Mises stress

i

1 14.!

tasns s^t jys 1!

iS!SiS!.?3

rrar- —i—

I. r

ci. en

= .643-04 ~ .Ksn-ss TM .iS2-0S

I L 1.

1 J_ 1 -_J

(in./in.)

T-iM

TE!tE«3i!tl

Jl'SSCS-Bst.

TV —.7144

JV ..6OT52

not -Z

A-!!"-. SM47t

(c) Plastic strain (d) Spandrel deformation at Floor 99

Figure 6-26. Structural response for temperature time history F with all floors supported.

Table 6-9. Summary of spandrel splice break elements for

Number of failed elements

Floor West Interior East Interior Splice

99 3 3 98 0 0

97 0 0

96 0 0

95 0 0

94 0 0

93 0 0

92 0 0

91 0 0

Total 3 3

184 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

6.7.2 Columns Not Braced at Floors 95 and 96

Analysis Case 6 (Fire Scenario DBARE) Figures 6-27 (a) and 6-27 (b) show the total displacement and von Mises stress, respectively, for the entire model. Figure 6-27 (a) shows that the maximum

displacement of 3.76 in. occurred above Floor 99. Figure 6-27 (b) indicates that the maximum von Mises

stress in the spandrels of 23 ksi occurred at Floor 94 between Columns 154 and 155. Figure 6-27 (c)

shows normal (transverse to the plane of the wall) displacement of the entire model. This figure shows a maximum outward displacement of 0.34 in. at Floor 96 and Column 154 and a maximum inward

displacement of 0.45 in. at Floor 95 and Column 158. Table 6-10 summarizes the status of the spandrel

splice break elements. Failed break elements at Floors 97 through 99 indicated tearing failure, and failed

break elements at Floors 96 and below indicated bolt shear failure.

<lliiitiNiiiiiiiMiikii

issrs 5.1 . :

*eit. IS KiOi , "«B^.MiW^* Gap

trnXi SCiHTKM

i ( !

i i ? T T t!K .S.1S9 SBS -iS. Ml mmm» : ? ; ; i. i M i

Km *toC!fe3S

. . a. 839 mMom ... 1

But M i i H

TM «iS3 SB1 .

(psi)

(c) Transverse displacement

(outward displacement is positive)

Figure 6-27. Structural response for temperature time history DBARE with two unbraced

floors.

NISTNCSTAR 1-6C, WTC Investigation 185
Chapter 6

Table 6-10. Summary of spandrel splice break elements for

temperature time history DBARE with 2 unbraced f oors. Number of failed elements

Floor West Interior Last Interior Splice

OQyy

1I

->

3 3 Q7y 1 1 U OA 11

1

1 yj 1 0

94 0 0

93 0 0

92 0 0

91 0 0

total 7 7

6.7.3 Columns Not Braced at Floors 95, 96, and 97

Analysis Case 7 (Fire Scenario DBARE) Figures 6-28 (a) and 6-28 (b) show the total displacement and von Mises stress, respectively, for the entire model. Figure 6-28 (a) shows that the maximum

displacement of 3.79 in. occuiTed above Floor 99. Figure 6-28 (b) indicates that the maximum von Mises

stress in the spandrels of 23 ksi occurred at Floor 94 between Columns 154 and 155. Figure 6-28 (c)

shows transverse to the plane of the wall displacement of the entire model. This figure shows a maximum

outward displacement of 0.21 in. at Floor 96 between Columns 154 and 155 and a maximum inward

displacement of 0.96 in. at Floor 96 and Column 158. Table 6-1 1 summarizes the status of the spandrel

splice break elements. Failed break elements at Floors 97 through 99 indicated tearing failure, and failed

break elements at Floors 96 and below indicated bolt shear failure.

186 NIST NCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

(c) Transverse displacement

(outward displacement is positive)

Figure 6-28. Structural response for time history DBARE with three unbraced floors.

Table 6-11. Spandrel splice break elements for temperature

time history DBARE with 3 unbraced floors.

Number of failed elements

Floor W est Interior Splice East Interior Splice

99 1 3 98 3 3 97 1 0 96 1 1 95 1 1 94 0 0 93 0 0 92 0 0

91 0 0

Total 7 8

NISTNCSTAR 1-6C, WTC Investigation 187
Chapter 6

6.7A Columns Not Braced and Pulled at Unbraced Floors 95, 96, and 97

Analysis Case 8 (Fire Scenario DBARE) Figures 6-29 (a) through 6-29 (d) show the total displacement, von Mises stress, and plastic strain, respectively, for the entire model. Figure 6-29 (a) shows that the

maximum displacement of 10.4 in. occurred at Floor 96. Figures 6-29 (b) through 6-29 (c) indicate that the maximum von Mises stress occurred at Floor 94 and Column 156. Figure 6-29 (d) shows that plastic

strain is limited to the portion of the spandrel at Floor 96 and Column 152. Figure 6-29 (e) shows

transverse (to the plane of the wall) displacement of the entire model. This figure shows a maximum

inward displacement of 10.2 in. at Floor 96. Figure 6-30 shows the maximum column splice bolt

stresses, which occurred between Floors 96 and 97 at Columns 156 through 158. Figure 6-31 shows

column splice contact status for those column splices occurring between Floors 94 and 97. This figure

indicates that column splices had opened or nearly opened at eight of the nine columns within this group

of floors.

188 NISTNCSTAR 1-6C. WTC Investigation
Exterior Wall Subsystem

77190

(psi)

(a) Total deflection (b) von Mises stress

AKSYS 8.1 JUL 21 200-1 NODAL SOLUTIOK

TiKE-5-101 EPPLEQV (AVG) ?owerGraphics

3MX -.581Z-03 g °s.,e.-o, 1

.129E:-03 .2SSE-03 22 .323E-03

SKALL-19

(in./in.)

(c) von Mises stress (d) Plastic strain

Iff SAViSi

s^1 '7. Si* —I -.5. «2'

-4. as TM -l.S*S

(e) Transverse displacennent

(outward displacennent is positive)

Figure 6-29. Structural response for temperature time history DBARE with pull-in forces

at three floors (10X displacement magnification).

NISTNCSTAR 1-6C, WTC Investigation 189
Chapter 6

Floor 97

Floor 96

158

1 1

- ^ k I

SWALL-19

1 2004

0 SOLUTION

AH SYS 8 JUL

11 : 42;

ELEMENT

STEP=31

SUB =22 TIME=S401

SX (NOAV ESYS=0 PowerGr aphi cs EFACET=1 DHX =9.

SUN =171 SHX =88S

I 1

CZ3

488 160

889

160

130

100

070

040

010 979

949

919

389

(psi)

Max. 88.9 ksi tension in bolts

Figure 6-30. Column splice bolt stresses for temperature time history and DBARE with

pull-in forces at three floors.

Floor 97

Floor 94

Blue (b) - open

Green (g)-~ sliding

Red (r) - sticking

AHSYS 8. 1 JUL 21 2004

11:11: 58 ELEMENT SOLUTION

STEf=31

SUE =22

TIIIE = J 401 NHISl

TOP rHX =10. 391 SHN =1

SIIX =3 Em

an

E21

.222

.444 .667

.889

.111

.333

. J S6 .778

Note: 1 contact element pair also sliding at Col. 155 b/w Floors 98 and 99

Figure 6-31. Column splice contact element status for temperature time history and

DBARE with pull-in forces at three floors.

190 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

6.7.5 Columns Not Braced at Floors 95, 96, and 97 and Pushed Down at Top

Analysis Case 9 (Fire Scenario DBARE) Figure 6-32 (a) shows that the maximum total displacement of

14.8 in. occurred at Floor 96. Figure 6-32 (b) indicates that the maximum von Mises stress of 69 ksi

occurred in Column 158 at Floor 96. Figure 6-32 (c) shows the von Mises stress in the spandrels and

indicates that the maximum stress of 32 ksi occurred at Floor 96 between Columns 151 and 152. Figures

6-33 (a) and 6-33 (b) show the column splice bolt stresses and column splice contact status, respectively.

The maximum column sphce bolt stress of 72 ksi occurred between Floors 94 and 95. Also, between

Floors 94 and 95 at Columns 150 through 152, one contact element had opened and five others were

shding by the end of the analysis. Figures 6-34 and 6-35 show the sum of total vertical reaction forces at base and the sum of additional vertical reaction force at base induced by push-down, respectively.

Figure 6-34 shows that instability occurred at a vertical displacement of 1.2 in., and columns unload

beyond the point of instability to the end of analysis. Figures 6-36 through 6-38 show the total vertical

reaction force, the additional vertical reaction force induced by push-down, and the difference between

the additional vertical reaction at the base and the additional vertical force applied to the top for each

column. Figure 6-38 shows that forces redistributed among the various columns throughout the pushdown loading. Figure 6-39 shows the transverse displacement at Column 154 with induced vertical

displacement.

All deformations, partial separations of spandrel splices, stresses, and strains presented above are at the

termination of the analyses after application of gravity loads, temperature time histories, and the imposed

vertical displacement of 2.0 in. and not at the point of instabilit>' with a vertical displacement of 1.2 in.

NISTNCSTAR 1-6C, WTC Investigation 191
Chapter 6

AN

ja. 29 304 < mm : om

: .t-v:-

(a) Total deflection

(psi)

(b) von MIses stress in columns

SWt -U13 SOT «V!S) £K«: -M.lrgS SMS -MS.lSe

29 2<liM sun m. 14

(psi)

(c) von Mises stress in spandrels

Figure 6-32. Structural response for temperature time history DBARE and push-down

with three unbraced floors (10X displacement magnification).

OSS "»J4>

36 j;

JiMJ

j

(psi)

(a) Maxinnum longitudinal stress in bolts

TSMB-SitlSS

cm "1

(b) Column splice contact element status

Figure 6-33. Column splice response for temperature time history DBARE and pushdown with three unbraced floors.

192 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

3000 c

0 0.5 1 1.5 2 Applied UZ at Tops of Columns (in.)

Figure 6-35. Sum of additional vertical reaction forces at base induced by imposed

displacement during push-down after application of temperature DBARE with three

unbraced floors.

NISTNCSTAR 1-6C, WTCInvestigation 193
Chapter 6

600000

0 1 0 0.5 1 1.5 2 Applied UZ at Tops of Columns (in.)

col 150 col 151 col 152 .<.~-col 153 col 154 col 155 col 156 col 157 —col 158

Figure 6-36. Individual total column reaction forces at base during push-down after

application of temperature DBARE with three unbraced floors.

360000

0 0.5 1 1.5 2

Applied UZ at Tops of Columns (in.)

col 150 ^col 151 col 152 - col 153 col 154 col 155 col 156

col 157 —.col 158

Figure 6-37. Individual additional column reaction forces at base induced by imposed

vertical displacement during push-down after application of temperature DBARE with

three unbraced floors.

194 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

40000

-30000 Applied UZ at Tops of Columns (in.)

col 150 col 151 ——col 152 —~col 153 col 154 col 155 ——col 156

col 157 ——col 158

Figure 6-38. Difference between the additional individual column reaction forces at base

and the vertical force applied at the top of each column during push-down after

application of temperature DBARE with three unbraced floors.

15

10

oa

o

c

Applied UZ at Tops of Columns (in.)

Figure 6-39. Transverse deflection during push-down after application of temperature

DBARE with three unbraced floors.

NISTNCSTAR 1-6C, WTC Investigation 195
Chapter 6

6.8 SUMMARY AND DISCUSSION OF EXTERIOR WALL ANALYSIS RESULTS

6.8.1 Columns Braced at All Floors

The analysis results presented above for the exterior wall subsystem with columns braced at all floors,

Analysis Case 1 through Case 5, indicate the following:

1 . Spandrels had the maximum stress in each Case.

2. The maximum spandrel stresses were at the columns.

3. The maximum spandrel strains were plastic.

4. Spandrels experienced large lateral distortions, indicative of lateral buckling.

5. Spandrel splices partially separated, but no spandrel splice separated completely in any of the

five Cases. Partial failure of spandrel splices typically indicated tearing failures at Floor 97

and above and bolt shear failures at Floor 96 and below.

6. Lateral deflections of columns did not exceed 1 in.

7. The principal contributor to the total vertical deflection of the columns was the unrestrained

vertical expansion due to thermal effects.

8. General instability of the exterior wall did not occur.

The model was unrestrained against in-plane deflection at both edges. In-plane deflection restraint from

the remaining wall can further increase the lateral distortions, possibly buckle the spandrels, and fail additional spandrel splices from thermal expansion effects.

6.8.2 Columns Not Braced at Floors 95 and 96

The analysis results for the exterior wall subsystem with columns not braced at Floors 95 and 96,

Analysis Case 6, indicate the following:

1 . Lateral deflections of the columns were less than 1 in.

2. There was no plastic strain in the columns and spandrels.

3. All column-splice contacts remained closed.

4. There was additional partial spandrel splice separation at Floors 95, 96, 97, and 99.

5. No spandrel splice separated completely. Partial failure of spandrel splices indicated tearing

failures at Floor 97 and above and bolt shear failures at Floor 96 and below.

6. General instability of the exterior wall did not occur.

6.8.3 Columns Not Braced at Floors 95, 96, and 97

The analysis results for the exterior wall subsystem with columns not braced at Floors 95, 96, and 97,

Analysis Case 7, indicate the following:

1 . Lateral deflections of the columns were less than 1 in.

2. There was no plastic strain in the columns and spandrels.

3. All column-splice contacts remained closed.

196 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

4. There was additional partial spandrel splice separation at Floors 95, 96, 97, and 99.

5. No spandrel splice separated completely. Partial failure of spandrel splices indicated tearing

failures at Floor 97 and above and bolt shear failures at Floor 96 and below.

6. General instabihty of the exterior wall did not occur.

6.8.4 Columns Not Braced and Pulled in at Floors 95, 96, and 97

The analysis results for the exterior wall subsystem with columns not braced at Floors 95, 96, and 97 and

subjected to pull-in force after DBARE temperature condition, Analysis Case 8, indicate the following:

1 . A converged solution could not be obtained at the point of instability with a pull-in force

greater than 12.6 kip.

2. At 12.6 kip pull-in force, the inward bowing of the exterior wall was 10.2 in.

3. The maximum column stress of 77.2 ksi was at Floor 94

4. Column-splice contacts slid or opened at several columns.

5. No column splice bolts fractured.

6. There were local plastic strains in the spandrel at Floor 94.

7. There \\'as additional partial spandrel splice plate separation at Floor 99, but no spandrel

splice separated completely.

8. Instability of the exterior wall with 12.6 kip pull-in force was likely for the temperature

condition at the end of DBARE temperature.

6.8.5 Columns Not Braced at Floors 95, 96, and 97 and Columns Pushed Down at Top

The analysis results for the exterior wall subsystem with columns not braced at Floors 95, 96, and 97 and

subjected to push-down displacement after DBARE temperature condition. Analysis Case 9, indicate the following:

1. The maximum sum of total reaction forces resulting from self weight, column and floor

loads, and push-down force and was 4,580 kip, for nine columns.

2. The maximum individual total column reaction force was approximately 570 kip.

3. The maximum sum of additional column reaction force induced from push-down was 2,710

kip for nine columns.

4. The maximum individual additional column reaction force induced from push-down was

approximately 350 kip.

5. Point of general instability, i.e. the maximum sum of column reaction forces was obtained at a push-down vertical deflection of 1.2 in.

6. The lateral deflection at point of instability was 5.2 in.

7. At an imposed downward vertical displacement of 2.0 in. (i.e., at the end of the push-down

analysis), the sum of additional vertical reaction forces was reduced from 2,710 kip to approximately 2,000 kip.

NISTNCSTAR 1-6C, WTC Investigation 19
Chapter 6

8. At an imposed downward vertical displacement of 2.0 in., the lateral deflection increased

from 5.2 in. at the maximum load to deflection 14.7 in.

9. Instability of the exterior wall was reached at a downward deflection of 1.2 in. when the

push-down force was approximately about 1 50 percent of the initial gravity dead and live loads.

6.8.6 Summary of Analysis Results

Table 6-12 provides a brief summary of the exterior wall model analysis results.

Table 6-12. Summary of exterior wall model results.

A niilv^i^ Case

Total Opflprtinn

(in.)

Maximum

Stress

(ksi) Plastic Strain?

Number of

Spandrel Splice

Break Element

Failures'

Spandrel Splice

Failure Type

1 1.53 49 YES 12 Tearing

2 3.74 49 YES 11 Tearing

3 1.87 57 YES 48 Tearing and Bolt Shear

4 2.07 53 YES 6 Tearing

5 1.57 46 YES 6 Tearing

6 3.76 23 NO 14 Tearing and Bolt

Shear

7 3.79 23 NO 15 Tearing and Bolt

Shear

8 10.4 77 YES

9 14.8 69 YES

' 198 total possible break element failures

6.9 SUMMARY OF RESULTS

The analyses of the exterior wall model support the following conclusions for modeling the towers:

1. Large inelastic deformations of the spandrels and buckling at elevated temperatures can be

expected, but they do not significantly affect the stability of the exterior columns and need

not be accurately modeled for the global analyses.

2. Partial separations of the spandrel splices can be expected at elevated temperatures, but they

do not significantly affect the stability of the exterior columns and need not be accurately

modeled for the global analyses.

3. Exterior column splices can be expected to fail by sliding or opening at elevated temperatures

and increased vertical loading. However, failure of column splices is expected only in the

final phases of collapse sequence and need not be accurately modeled for global analyses.

4. Instability of exterior wall subsystem is expected when at least three floors are unbraced and

the exterior wall subsystem is subjected to additional vertical load or pull-in forces.

198 NISTNCSTAR 1-6C, WTC Investigation
Exterior Wall Subsystem

5. Plastic buckling by kinking with rapid reduction of load capacity in the post-buckling regime

of exterior columns is expected at high column loads and at low temperatures. At lower loads

and at high temperatures, plastic buckling with some reduction of load-carrying capacity as expected by P-delta effect occurs. Hence, the kinking-type plastic buckling need not be

accurately modeled for global models.

NISTNCSTAR 1-6C, WTC Investigation 199
Chapter 6

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200 NISTNCSTAR 1-6C, WTC Investigation
Chapter 7

Modeling Details for Subsystems in Global Models

Structural analyses performed for components, connections, and subsystems revealed their key structural responses and failure modes. The results of analyses performed on the exterior wall subsystem showed

that when the exterior wall subsystem was subjected to fires it would become unstable either when three or more floors were disconnected from the exterior wall and the exterior wall was subjected to additional

vertical loads or when sagging floors exerted pull-in forces on the exterior wall. The results of the full floor subsystem analyses showed that the floor disconnected from the exterior wall when the sagging

floor walked off the truss seat or the exterior truss seat failed under the combined action of vertical gravity loads and high temperatures.

Based on the results of the finite-element analyses performed on components, connections, and

subsystems, a decision was made to use the following modeling details for the subsystems in the global

models to enhance numerical efficiency.

Floor Subsystem

Floors in the global model were modeled by shell elements, which have their membrane stiffness equal to that of the full floor system. Floors in the global model function as diaphragms and transfer load between

the exterior wall system and the core.

The global model cannot be constructed with the same level of detail in all floors subjected to thermal

loading as the full floor model developed in this report. It was not practical, or in some cases not

possible, to create computationally efficient global models that included all details of the floor system.

The BEAM188/189 elements used in the full floor model caused severe convergence problems when

creep was included and those elements experience thermally-induced buckling. Also, the extent of pull-in

forces from sagging floors in the full floor models was less than estimated from the observed bowing of

the exterior walls in photographs and videos because the aircraft impact damage to thermal insulation of

the floors was conser\'atively estimated by limiting the dislodged thermal insulation to regions of direct debris impact.

To enhance computational efficiency and perform the computations in a reasonable time span, it was

decided to model the pull-in forces and disconnections of floors from the exterior walls in the global

models as "fire-induced damage" at appropriate times. Since the full floor models did not accurately

estimate the pull-in forces at floor/wall connections, the fire-induced damage obtained from the full floor model analyses were modified by "actual observations" obtained from the examination of photographs

and videos performed by NIST (NIST NCSTAR 1-5 A).

Exterior Wall Subsystem

The exterior and interior columns were modeled with fidelity of their inelastic buckling behavior. To

capture the premamre buckling of the single span exterior columns at low temperatures, which would

occur at the onset of plate buckling and results in kinking of the cross section, a fine mesh was needed.

However, observations of photographs and videos showed that bowing was extended over several floors

NIST NCSTAR 1-6C, WTC Investigation 201
Chapter 7

and column temperatures were not low. Therefore, kink-type buckling of the exterior columns was

neglected, and was not modeled.

Exterior column splices were not modeled in the global models as failure of columns splices did not occur

in the exterior wall subsystem analyses and was not obserx'ed in either tower prior to collapse initiation.

Spandrels were modeled by beam elements capable of resisting shear and bending moment. The spandrel

splices were not modeled in the global analyses as complete separation of spandrel splices did not occur

in the exterior wall studies and was not observed in either tower prior to collapse initiation.

202 NISTNCSTAR 1-6C, WTC Investigation
Chapter 8

References

ACI Committee 209 (1992), "Prediction of Creep, Shrinkage, and Temperature Effects in Concrete

Strucmres," A CI 209R-92, ACI.

ACI Committee 3 1 8 (2002), "Building Code Requirements for Structural Concrete and Commentary,"

ACI 318-02, ACI.

American Institute for Steel Construction (2003), Manual ofSteel Construction, Load and Resistance

Factor Design, 3rd Edition, AISC.

American Instimte for Steel Constmction (2001), Manual ofSteel Constiniction, Load and Resistance

Factor Design, 2nd Edition, AISC.

American Institute for Steel Construction (1964), Manual ofSteel Construction, Allowable Stress Design,

6th Edition. AISC.

ANSYS, Inc. 2004. ANSYS Release 8.1 Documentation. ANSYS, Inc., Canonsburg, PA.

ANSYS, Inc. 2004. Theoiy Reference, ANSYS, Inc.

Bartlett. F. M. and MacGregor, J. G. (1996), "Statistical Analysis of the Compressive Strength of

Concrete in Structures," ACI Materials Journal, March-April, pp. 158-168.

Fields, B. A. and Fields, R. J. (1991), The Prediction ofElevated Temperature Deformation ofStructural

Steel Under Anisothermal Conditions, NIST.

LERA (2003), Development ofStructural Databases and Baseline Models for the World Trade Center

(WTC) Towers - Progress Report #4: Structural Analysis Computer Models.

Livermore Software Technology Corporation. 2003. LS-DYNA User's Manual. Livermore Software

Technology Corporation. Livermore, CA.

Phan, Long T. (1996), Fire Performance ofHigh-Strength Concrete: A Report ofthe State-of-the-Art,

NIST.

Seanz, L. P. (1964). "Discussion of Equation of the Stress-Strain Curve of Concrete by Desayi and

Krishman," Journal ofthe .American Concrete Institute, Col. 61 , No. 9, pp. 1229-1235.

Stevick, G. R. (1994), "Failure of Welds at Elevated Temperatures," Welded Research Council

Bulletin 390, Welding Research Council, pp. 1-39.

NISTNCSTAR 1-6C, WTC Investigation 203
Chapter 8

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204 NISTNCSTAR 1-6C, WTC Investigation


NIST NCSTAR1-6C

Federal Building and Fire Safety Investigation of the

World Trade Center Disaster

Component, Connection, and

Subsystem Structural Analysis

Mehdi S. Zarghamee,

Said Bolourchi

Daniel W. Eggers

Omer 0. Erbay

Frank W. Kan

Yasuo Kitane

Peter R. Barrett

John L. Gross

Therese P. McAllister

Atis A. Liepins

Michael Mudlock

Wassim I. Naguib

Rasko P. Ojdrovic

Andrew T. Sarawit

National Institute of Standards and Technology • Technology Adminlslralion • U.S. Department of Commerce